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{{Redirect|IQR}}
[[Image:Boxplot vs PDF.svg|250px|thumb|[[Boxplot]] (with an interquartile range) and a [[probability density function]] (pdf) of a Normal {{maths|N(0,σ<sup>2</sup>)}} Population]]
In [[descriptive statistics]], the '''interquartile range''' ('''IQR''') is a measure of [[statistical dispersion]], which is the spread of the data.<ref name=":1">{{Cite book|last=Dekking|first=Frederik Michel|url=http://link.springer.com/10.1007/1-84628-168-7|title=A Modern Introduction to Probability and Statistics|last2=Kraaikamp|first2=Cornelis|last3=Lopuhaä|first3=Hen Paul|last4=Meester|first4=Ludolf Erwin|date=2005|publisher=Springer London|isbn=978-1-85233-896-1|series=Springer Texts in Statistics|location=London|doi=10.1007/1-84628-168-7}}</ref> The IQR may also be called the '''midspread''', '''middle 50%''', '''fourth spread''', or L'''‑spread.''' It is defined as the difference between the 75th and 25th [[percentiles]] of the data.<ref name="Upton" /><ref name="ZK" /><ref>{{Cite book|last=Ross|first=Sheldon|title=Introductory Statistics|publisher=Elsevier|year=2010|isbn=978-0-12-374388-6|location=Burlington, MA|pages=103–104}}</ref> To calculate the IQR, the data set is divided into [[quartile]]s, or four rank-ordered even parts via linear interpolation.<ref name=":1" /> These quartiles are denoted by Q<sub>1</sub> (also called the lower quartile), ''Q''<sub>2</sub> (the [[median]]), and ''Q''<sub>3</sub> (also called the upper quartile). The lower quartile corresponds with the 25th percentile and the upper quartile corresponds with the 75th percentile, so IQR = ''Q''<sub>3</sub> − ''Q''<sub>1</sub><ref name=":1" /><sub>.</sub>
The IQR is an example of a [[trimmed estimator]], defined as the 25% trimmed [[Range (statistics)|range]], which enhances the accuracy of dataset statistics by dropping lower contribution, outlying points.<ref name=":2">{{Cite book|last=Kaltenbach|first=Hans-Michael|url=https://www.worldcat.org/oclc/763157853|title=A concise guide to statistics|date=2012|publisher=Springer|isbn=978-3-642-23502-3|location=Heidelberg|oclc=763157853}}</ref> It is also used as a [[Robust measures of scale|robust measure of scale]]<ref name=":2" /> It can be clearly visualized by the box on a [[box plot]].<ref name=":1" />
==Use==
Unlike total [[range (statistics)|range]], the interquartile range has a [[breakdown point]] of 25%<ref>{{cite news |title=Explicit Scale Estimators with High Breakdown Point |first1=Peter J. |last1=Rousseeuw |first2=Christophe |last2=Croux |work=L1-Statistical Analysis and Related Methods |editor=Y. Dodge |location=Amsterdam |publisher=North-Holland |year=1992 |pages=77–92 |url=https://feb.kuleuven.be/public/u0017833/PDF-FILES/l11992.pdf}}</ref> and is thus often preferred to the total range.
The IQR is used to build [[box plot]]s, simple graphical representations of a [[probability distribution]].
The IQR is used in businesses as a marker for their [[income]] rates.
For a symmetric distribution (where the median equals the [[midhinge]], the average of the first and third quartiles), half the IQR equals the [[median absolute deviation]] (MAD).
The [[median]] is the corresponding measure of [[central tendency]].
The IQR can be used to identify [[outlier]]s (see [[#Outliers|below]]). The IQR also may indicate the [[skewness]] of the dataset.<ref name=":1"/>
{{Anchor|Quartile deviation}} The quartile deviation or semi-interquartile range is defined as half the IQR.<ref name="Yule">{{cite book |first=G. Udny |last=Yule |title=An Introduction to the Theory of Statistics |url=https://archive.org/details/in.ernet.dli.2015.223539 |publisher=Charles Griffin and Company |date=1911 |pages=[https://archive.org/details/in.ernet.dli.2015.223539/page/n170 147]–148}}</ref>
==Algorithm==
The IQR of a set of values is calculated as the difference between the upper and lower quartiles, Q<sub>3</sub> and Q<sub>1</sub>. Each quartile is a median<ref name=":0">{{Cite book|title=Beta [beta] mathematics handbook : concepts, theorems, methods, algorithms, formulas, graphs, tables|last=Bertil.|first=Westergren|date=1988|publisher=[[Studentlitteratur]]|isbn=9144250517|oclc=18454776|page=348}}</ref> calculated as follows.
Given an even ''2n'' or odd ''2n+1'' number of values
:''first quartile Q<sub>1</sub>'' = median of the ''n'' smallest values
:''third quartile Q<sub>3</sub>'' = median of the ''n'' largest values<ref name=":0" />
The ''second quartile Q<sub>2</sub>'' is the same as the ordinary median.<ref name=":0" />
==Examples==
===Data set in a table===
The following table has 13 rows, and follows the rules for the odd number of entries.
{| class="wikitable" style="text-align:center;"
|-
! width="40px" | i
! width="40px" |x[i]
! Median
! Quartile
|-
| 1
| 7
| rowspan="14" |Q<sub>2</sub>=87<br /> (median of whole table)
| rowspan="6" |Q<sub>1</sub>=31<br /> (median of lower half, from row 1 to 6)
|-
| 2
| 7
|-
| 3
| 31
|-
| 4
| 31
|-
| 5
| 47
|-
| 6
| 75
|-
| 7
| 87
|
|-
| 8
| 115
| rowspan="6" | Q<sub>3</sub>=119<br /> (median of upper half, from row 8 to 13)
|-
| 9
| 116
|-
| 10
| 119
|-
| 11
|119
|-
| 12
| 155
|-
| 13
| 177
|}
For the data in this table the interquartile range is IQR = Q<sub>3</sub> − Q<sub>1</sub> = 119 - 31 = 88.
===Data set in a plain-text box plot===
<pre style="font-family:monospace">
+−−−−−+−+
* |−−−−−−−−−−−| | |−−−−−−−−−−−|
+−−−−−+−+
+−−−+−−−+−−−+−−−+−−−+−−−+−−−+−−−+−−−+−−−+−−−+−−−+ number line
0 1 2 3 4 5 6 7 8 9 10 11 12
</pre>
For the data set in this [[box plot]]:
* Lower (first) quartile ''Q''<sub>1</sub> = 7
* Median (second quartile) ''Q''<sub>2</sub> = 8.5
* Upper (third) quartile ''Q''<sub>3</sub> = 9
* Interquartile range, IQR = ''Q''<sub>3</sub> - ''Q''<sub>1</sub> = 2
* Lower 1.5*IQR whisker = ''Q''<sub>1</sub> - 1.5 * IQR = 7 - 3 = 4. (If there is no data point at 4, then the lowest point greater than 4.)
* Upper 1.5*IQR whisker = ''Q''<sub>3</sub> + 1.5 * IQR = 9 + 3 = 12. (If there is no data point at 12, then the highest point less than 12.)
* Pattern of latter two bullet points: If there are no data points at the true quartiles, use data points slightly "inland" (closer to the median) from the actual quartiles.
This means the 1.5*IQR whiskers can be uneven in lengths. The median, minimum, maximum, and the first and third quartile constitute the [[Five-number summary]].<ref>Dekking, Kraaikamp, Lopuhaä & Meester, pp. 235–237</ref>
==Distributions==
The interquartile range of a continuous distribution can be calculated by integrating the [[probability density function]] (which yields the [[cumulative distribution function]]—any other means of calculating the CDF will also work). The lower quartile, ''Q''<sub>1</sub>, is a number such that integral of the PDF from -∞ to ''Q''<sub>1</sub> equals 0.25, while the upper quartile, ''Q''<sub>3</sub>, is such a number that the integral from -∞ to ''Q''<sub>3</sub> equals 0.75; in terms of the CDF, the quartiles can be defined as follows:
:<math>Q_1 = \text{CDF}^{-1}(0.25) ,</math>
:<math>Q_3 = \text{CDF}^{-1}(0.75) ,</math>
where CDF<sup>−1</sup> is the [[quantile function]].
The interquartile range and median of some common distributions are shown below
{| class="wikitable"
|-
! Distribution
! Median
! IQR
|-
| [[Normal distribution|Normal]]
| μ
| 2 Φ<sup>−1</sup>(0.75)σ ≈ 1.349σ ≈ (27/20)σ
|-
| [[Laplace distribution|Laplace]]
| μ
| 2''b'' ln(2) ≈ 1.386''b''
|-
| [[Cauchy distribution|Cauchy]]
| μ
|2γ
|}
===Interquartile range test for normality of distribution===
The IQR, [[mean]], and [[standard deviation]] of a population ''P'' can be used in a simple test of whether or not ''P'' is [[Normal distribution|normally distributed]], or Gaussian. If ''P'' is normally distributed, then the [[standard score]] of the first quartile, ''z''<sub>1</sub>, is −0.67, and the standard score of the third quartile, ''z''<sub>3</sub>, is +0.67. Given ''mean'' = <math>\bar{P}</math> and ''standard deviation'' = σ for ''P'', if ''P'' is normally distributed, the first quartile
:<math>Q_1 = (\sigma \, z_1) + \bar{P}</math>
and the third quartile
:<math>Q_3 = (\sigma \, z_3) + \bar{P}</math>
If the actual values of the first or third quartiles differ substantially{{Clarify|date=December 2012}} from the calculated values, ''P'' is not normally distributed. However, a normal distribution can be trivially perturbed to maintain its Q1 and Q2 std. scores at 0.67 and −0.67 and not be normally distributed (so the above test would produce a false positive). A better test of normality, such as [[Q–Q plot]] would be indicated here.
==Outliers==
[[File:Box-Plot mit Interquartilsabstand.png|thumb|[[Box-and-whisker plot]] with four mild outliers and one extreme outlier. In this chart, outliers are defined as mild above Q3 + 1.5 IQR and extreme above Q3 + 3 IQR.]]
The interquartile range is often used to find [[outlier]]s in data. Outliers here are defined as observations that fall below Q1 − 1.5 IQR or above Q3 + 1.5 IQR. In a boxplot, the highest and lowest occurring value within this limit are indicated by ''whiskers'' of the box (frequently with an additional bar at the end of the whisker) and any outliers as individual points.
==See also==
* {{Annotated link|Interdecile range}}
* {{Annotated link|Midhinge}}
* {{Annotated link|Probable error}}
* {{Annotated link|Robust measures of scale}}
==References==
{{reflist|refs=
<ref name=Upton>{{cite book |title=Understanding Statistics |first1=Graham|last1=Upton|first2=Ian|last2= Cook|year=1996 |publisher=Oxford University Press |isbn=0-19-914391-9 |page=55 |url=https://books.google.com/books?id=vXzWG09_SzAC&q=interquartile+range&pg=PA55}}</ref>
<ref name= ZK>Zwillinger, D., Kokoska, S. (2000) ''CRC Standard Probability and Statistics Tables and Formulae'', CRC Press. {{ISBN|1-58488-059-7}} page 18.</ref>
}}
==External links==
*{{Commonscatinline}}
{{Statistics|descriptive}}
{{DEFAULTSORT:Interquartile Range}}
[[Category:Scale statistics]]
[[Category:Wikipedia articles with ASCII art]]' |
New page wikitext, after the edit (new_wikitext) | '{{Short description|Measure of statistical dispersion}}
{{Redirect|IQR}}
[[Image:Boxplot vs PDF.svg|250px|thumb|[[File:Skibidi Toilet fan-art.jpg|thumb|sigma rizz 999]]Skibidi Rizz 999 graph]]
Why am I sigma? 6 reasons 999
# '''Self-Reliance''':
#* Sigmas can function well in social groups if needed, but they also enjoy spending time alone.
#* They don’t depend on others and are comfortable being their own best friend.
# '''Emotional Independence''':
#* Sigmas don’t rely on external validation for happiness or completeness.
#* They take full responsibility for their own feelings.
# '''Authenticity''':
#* Authenticity is a common trait among sigmas.
#* They are genuine, comfortable in their own skin, and don’t pretend to be someone they’re not.
# '''Quiet Confidence''':
#* Sigmas may not appear extremely confident like alphas, but they have strong self-esteem.
#* Their quiet demeanor often hides their inner confidence.
# '''Success-Oriented''':
#* Sigmas tend to be successful because of their self-reliance, ambition, and determination.
#* They know what they want and pursue it relentlessly.
# '''Great Listeners''':
#* Their introverted nature allows them to listen attentively to others.
Remember that being a sigma is not better or worse than other personality types—it’s simply a unique combination of traits. Embrace your individuality and continue to grow!
The IQR is an example of a [[trimmed estimator]], defined as the 25% trimmed [[Range (statistics)|range]], which enhances the accuracy of dataset statistics by dropping lower contribution, outlying points.<ref name=":2">{{Cite book|last=Kaltenbach|first=Hans-Michael|url=https://www.worldcat.org/oclc/763157853|title=A concise guide to statistics|date=2012|publisher=Springer|isbn=978-3-642-23502-3|location=Heidelberg|oclc=763157853}}</ref> It is also used as a [[Robust measures of scale|robust measure of scale]]<ref name=":2" /> It can be clearly visualized by the box on a [[box plot]].<ref name=":1">{{Cite book |last=Dekking |first=Frederik Michel |url=http://link.springer.com/10.1007/1-84628-168-7 |title=A Modern Introduction to Probability and Statistics |last2=Kraaikamp |first2=Cornelis |last3=Lopuhaä |first3=Hen Paul |last4=Meester |first4=Ludolf Erwin |date=2005 |publisher=Springer London |isbn=978-1-85233-896-1 |series=Springer Texts in Statistics |location=London |doi=10.1007/1-84628-168-7}}</ref>
==Use==
Unlike total [[range (statistics)|range]], the interquartile range has a [[breakdown point]] of 25%<ref>{{cite news |title=Explicit Scale Estimators with High Breakdown Point |first1=Peter J. |last1=Rousseeuw |first2=Christophe |last2=Croux |work=L1-Statistical Analysis and Related Methods |editor=Y. Dodge |location=Amsterdam |publisher=North-Holland |year=1992 |pages=77–92 |url=https://feb.kuleuven.be/public/u0017833/PDF-FILES/l11992.pdf}}</ref> and is thus often preferred to the total range.
The IQR is used to build [[box plot]]s, simple graphical representations of a [[probability distribution]].
The IQR is used in businesses as a marker for their [[income]] rates.
For a symmetric distribution (where the median equals the [[midhinge]], the average of the first and third quartiles), half the IQR equals the [[median absolute deviation]] (MAD).
The [[median]] is the corresponding measure of [[central tendency]].
The IQR can be used to identify [[outlier]]s (see [[#Outliers|below]]). The IQR also may indicate the [[skewness]] of the dataset.<ref name=":1"/>
{{Anchor|Quartile deviation}} The quartile deviation or semi-interquartile range is defined as half the IQR.<ref name="Yule">{{cite book |first=G. Udny |last=Yule |title=An Introduction to the Theory of Statistics |url=https://archive.org/details/in.ernet.dli.2015.223539 |publisher=Charles Griffin and Company |date=1911 |pages=[https://archive.org/details/in.ernet.dli.2015.223539/page/n170 147]–148}}</ref>
==Algorithm==
The IQR of a set of values is calculated as the difference between the upper and lower quartiles, Q<sub>3</sub> and Q<sub>1</sub>. Each quartile is a median<ref name=":0">{{Cite book|title=Beta [beta] mathematics handbook : concepts, theorems, methods, algorithms, formulas, graphs, tables|last=Bertil.|first=Westergren|date=1988|publisher=[[Studentlitteratur]]|isbn=9144250517|oclc=18454776|page=348}}</ref> calculated as follows.
Given an even ''2n'' or odd ''2n+1'' number of values
:''first quartile Q<sub>1</sub>'' = median of the ''n'' smallest values
:''third quartile Q<sub>3</sub>'' = median of the ''n'' largest values<ref name=":0" />
The ''second quartile Q<sub>2</sub>'' is the same as the ordinary median.<ref name=":0" />
==Examples==
===Data set in a table===
The following table has 13 rows, and follows the rules for the odd number of entries.
{| class="wikitable" style="text-align:center;"
|-
! width="40px" | i
! width="40px" |x[i]
! Median
! Quartile
|-
| 1
| 7
| rowspan="14" |Q<sub>2</sub>=87<br /> (median of whole table)
| rowspan="6" |Q<sub>1</sub>=31<br /> (median of lower half, from row 1 to 6)
|-
| 2
| 7
|-
| 3
| 31
|-
| 4
| 31
|-
| 5
| 47
|-
| 6
| 75
|-
| 7
| 87
|
|-
| 8
| 115
| rowspan="6" | Q<sub>3</sub>=119<br /> (median of upper half, from row 8 to 13)
|-
| 9
| 116
|-
| 10
| 119
|-
| 11
|119
|-
| 12
| 155
|-
| 13
| 177
|}
For the data in this table the interquartile range is IQR = Q<sub>3</sub> − Q<sub>1</sub> = 119 - 31 = 88.
===Data set in a plain-text box plot===
<pre style="font-family:monospace">
+−−−−−+−+
* |−−−−−−−−−−−| | |−−−−−−−−−−−|
+−−−−−+−+
+−−−+−−−+−−−+−−−+−−−+−−−+−−−+−−−+−−−+−−−+−−−+−−−+ number line
0 1 2 3 4 5 6 7 8 9 10 11 12
</pre>
For the data set in this [[box plot]]:
* Lower (first) quartile ''Q''<sub>1</sub> = 7
* Median (second quartile) ''Q''<sub>2</sub> = 8.5
* Upper (third) quartile ''Q''<sub>3</sub> = 9
* Interquartile range, IQR = ''Q''<sub>3</sub> - ''Q''<sub>1</sub> = 2
* Lower 1.5*IQR whisker = ''Q''<sub>1</sub> - 1.5 * IQR = 7 - 3 = 4. (If there is no data point at 4, then the lowest point greater than 4.)
* Upper 1.5*IQR whisker = ''Q''<sub>3</sub> + 1.5 * IQR = 9 + 3 = 12. (If there is no data point at 12, then the highest point less than 12.)
* Pattern of latter two bullet points: If there are no data points at the true quartiles, use data points slightly "inland" (closer to the median) from the actual quartiles.
This means the 1.5*IQR whiskers can be uneven in lengths. The median, minimum, maximum, and the first and third quartile constitute the [[Five-number summary]].<ref>Dekking, Kraaikamp, Lopuhaä & Meester, pp. 235–237</ref>
==Distributions==
The interquartile range of a continuous distribution can be calculated by integrating the [[probability density function]] (which yields the [[cumulative distribution function]]—any other means of calculating the CDF will also work). The lower quartile, ''Q''<sub>1</sub>, is a number such that integral of the PDF from -∞ to ''Q''<sub>1</sub> equals 0.25, while the upper quartile, ''Q''<sub>3</sub>, is such a number that the integral from -∞ to ''Q''<sub>3</sub> equals 0.75; in terms of the CDF, the quartiles can be defined as follows:
:<math>Q_1 = \text{CDF}^{-1}(0.25) ,</math>
:<math>Q_3 = \text{CDF}^{-1}(0.75) ,</math>
where CDF<sup>−1</sup> is the [[quantile function]].
The interquartile range and median of some common distributions are shown below
{| class="wikitable"
|-
! Distribution
! Median
! IQR
|-
| [[Normal distribution|Normal]]
| μ
| 2 Φ<sup>−1</sup>(0.75)σ ≈ 1.349σ ≈ (27/20)σ
|-
| [[Laplace distribution|Laplace]]
| μ
| 2''b'' ln(2) ≈ 1.386''b''
|-
| [[Cauchy distribution|Cauchy]]
| μ
|2γ
|}
===Interquartile range test for normality of distribution===
The IQR, [[mean]], and [[standard deviation]] of a population ''P'' can be used in a simple test of whether or not ''P'' is [[Normal distribution|normally distributed]], or Gaussian. If ''P'' is normally distributed, then the [[standard score]] of the first quartile, ''z''<sub>1</sub>, is −0.67, and the standard score of the third quartile, ''z''<sub>3</sub>, is +0.67. Given ''mean'' = <math>\bar{P}</math> and ''standard deviation'' = σ for ''P'', if ''P'' is normally distributed, the first quartile
:<math>Q_1 = (\sigma \, z_1) + \bar{P}</math>
and the third quartile
:<math>Q_3 = (\sigma \, z_3) + \bar{P}</math>
If the actual values of the first or third quartiles differ substantially{{Clarify|date=December 2012}} from the calculated values, ''P'' is not normally distributed. However, a normal distribution can be trivially perturbed to maintain its Q1 and Q2 std. scores at 0.67 and −0.67 and not be normally distributed (so the above test would produce a false positive). A better test of normality, such as [[Q–Q plot]] would be indicated here.
==Outliers==
[[File:Box-Plot mit Interquartilsabstand.png|thumb|[[Box-and-whisker plot]] with four mild outliers and one extreme outlier. In this chart, outliers are defined as mild above Q3 + 1.5 IQR and extreme above Q3 + 3 IQR.]]
The interquartile range is often used to find [[outlier]]s in data. Outliers here are defined as observations that fall below Q1 − 1.5 IQR or above Q3 + 1.5 IQR. In a boxplot, the highest and lowest occurring value within this limit are indicated by ''whiskers'' of the box (frequently with an additional bar at the end of the whisker) and any outliers as individual points.
==See also==
* {{Annotated link|Interdecile range}}
* {{Annotated link|Midhinge}}
* {{Annotated link|Probable error}}
* {{Annotated link|Robust measures of scale}}
==References==
{{reflist|refs=
<ref name=Upton>{{cite book |title=Understanding Statistics |first1=Graham|last1=Upton|first2=Ian|last2= Cook|year=1996 |publisher=Oxford University Press |isbn=0-19-914391-9 |page=55 |url=https://books.google.com/books?id=vXzWG09_SzAC&q=interquartile+range&pg=PA55}}</ref>
<ref name= ZK>Zwillinger, D., Kokoska, S. (2000) ''CRC Standard Probability and Statistics Tables and Formulae'', CRC Press. {{ISBN|1-58488-059-7}} page 18.</ref>
}}
==External links==
*{{Commonscatinline}}
{{Statistics|descriptive}}
{{DEFAULTSORT:Interquartile Range}}
[[Category:Scale statistics]]
[[Category:Wikipedia articles with ASCII art]]' |
Unified diff of changes made by edit (edit_diff) | '@@ -1,9 +1,29 @@
{{Short description|Measure of statistical dispersion}}
{{Redirect|IQR}}
-[[Image:Boxplot vs PDF.svg|250px|thumb|[[Boxplot]] (with an interquartile range) and a [[probability density function]] (pdf) of a Normal {{maths|N(0,σ<sup>2</sup>)}} Population]]
+[[Image:Boxplot vs PDF.svg|250px|thumb|[[File:Skibidi Toilet fan-art.jpg|thumb|sigma rizz 999]]Skibidi Rizz 999 graph]]
-In [[descriptive statistics]], the '''interquartile range''' ('''IQR''') is a measure of [[statistical dispersion]], which is the spread of the data.<ref name=":1">{{Cite book|last=Dekking|first=Frederik Michel|url=http://link.springer.com/10.1007/1-84628-168-7|title=A Modern Introduction to Probability and Statistics|last2=Kraaikamp|first2=Cornelis|last3=Lopuhaä|first3=Hen Paul|last4=Meester|first4=Ludolf Erwin|date=2005|publisher=Springer London|isbn=978-1-85233-896-1|series=Springer Texts in Statistics|location=London|doi=10.1007/1-84628-168-7}}</ref> The IQR may also be called the '''midspread''', '''middle 50%''', '''fourth spread''', or L'''‑spread.''' It is defined as the difference between the 75th and 25th [[percentiles]] of the data.<ref name="Upton" /><ref name="ZK" /><ref>{{Cite book|last=Ross|first=Sheldon|title=Introductory Statistics|publisher=Elsevier|year=2010|isbn=978-0-12-374388-6|location=Burlington, MA|pages=103–104}}</ref> To calculate the IQR, the data set is divided into [[quartile]]s, or four rank-ordered even parts via linear interpolation.<ref name=":1" /> These quartiles are denoted by Q<sub>1</sub> (also called the lower quartile), ''Q''<sub>2</sub> (the [[median]]), and ''Q''<sub>3</sub> (also called the upper quartile). The lower quartile corresponds with the 25th percentile and the upper quartile corresponds with the 75th percentile, so IQR = ''Q''<sub>3</sub> − ''Q''<sub>1</sub><ref name=":1" /><sub>.</sub>
+Why am I sigma? 6 reasons 999
-The IQR is an example of a [[trimmed estimator]], defined as the 25% trimmed [[Range (statistics)|range]], which enhances the accuracy of dataset statistics by dropping lower contribution, outlying points.<ref name=":2">{{Cite book|last=Kaltenbach|first=Hans-Michael|url=https://www.worldcat.org/oclc/763157853|title=A concise guide to statistics|date=2012|publisher=Springer|isbn=978-3-642-23502-3|location=Heidelberg|oclc=763157853}}</ref> It is also used as a [[Robust measures of scale|robust measure of scale]]<ref name=":2" /> It can be clearly visualized by the box on a [[box plot]].<ref name=":1" />
+# '''Self-Reliance''':
+#* Sigmas can function well in social groups if needed, but they also enjoy spending time alone.
+#* They don’t depend on others and are comfortable being their own best friend.
+# '''Emotional Independence''':
+#* Sigmas don’t rely on external validation for happiness or completeness.
+#* They take full responsibility for their own feelings.
+# '''Authenticity''':
+#* Authenticity is a common trait among sigmas.
+#* They are genuine, comfortable in their own skin, and don’t pretend to be someone they’re not.
+# '''Quiet Confidence''':
+#* Sigmas may not appear extremely confident like alphas, but they have strong self-esteem.
+#* Their quiet demeanor often hides their inner confidence.
+# '''Success-Oriented''':
+#* Sigmas tend to be successful because of their self-reliance, ambition, and determination.
+#* They know what they want and pursue it relentlessly.
+# '''Great Listeners''':
+#* Their introverted nature allows them to listen attentively to others.
+
+Remember that being a sigma is not better or worse than other personality types—it’s simply a unique combination of traits. Embrace your individuality and continue to grow!
+
+The IQR is an example of a [[trimmed estimator]], defined as the 25% trimmed [[Range (statistics)|range]], which enhances the accuracy of dataset statistics by dropping lower contribution, outlying points.<ref name=":2">{{Cite book|last=Kaltenbach|first=Hans-Michael|url=https://www.worldcat.org/oclc/763157853|title=A concise guide to statistics|date=2012|publisher=Springer|isbn=978-3-642-23502-3|location=Heidelberg|oclc=763157853}}</ref> It is also used as a [[Robust measures of scale|robust measure of scale]]<ref name=":2" /> It can be clearly visualized by the box on a [[box plot]].<ref name=":1">{{Cite book |last=Dekking |first=Frederik Michel |url=http://link.springer.com/10.1007/1-84628-168-7 |title=A Modern Introduction to Probability and Statistics |last2=Kraaikamp |first2=Cornelis |last3=Lopuhaä |first3=Hen Paul |last4=Meester |first4=Ludolf Erwin |date=2005 |publisher=Springer London |isbn=978-1-85233-896-1 |series=Springer Texts in Statistics |location=London |doi=10.1007/1-84628-168-7}}</ref>
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22 => 'The IQR is an example of a [[trimmed estimator]], defined as the 25% trimmed [[Range (statistics)|range]], which enhances the accuracy of dataset statistics by dropping lower contribution, outlying points.<ref name=":2">{{Cite book|last=Kaltenbach|first=Hans-Michael|url=https://www.worldcat.org/oclc/763157853|title=A concise guide to statistics|date=2012|publisher=Springer|isbn=978-3-642-23502-3|location=Heidelberg|oclc=763157853}}</ref> It is also used as a [[Robust measures of scale|robust measure of scale]]<ref name=":2" /> It can be clearly visualized by the box on a [[box plot]].<ref name=":1">{{Cite book |last=Dekking |first=Frederik Michel |url=http://link.springer.com/10.1007/1-84628-168-7 |title=A Modern Introduction to Probability and Statistics |last2=Kraaikamp |first2=Cornelis |last3=Lopuhaä |first3=Hen Paul |last4=Meester |first4=Ludolf Erwin |date=2005 |publisher=Springer London |isbn=978-1-85233-896-1 |series=Springer Texts in Statistics |location=London |doi=10.1007/1-84628-168-7}}</ref>'
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0 => '[[Image:Boxplot vs PDF.svg|250px|thumb|[[Boxplot]] (with an interquartile range) and a [[probability density function]] (pdf) of a Normal {{maths|N(0,σ<sup>2</sup>)}} Population]]',
1 => 'In [[descriptive statistics]], the '''interquartile range''' ('''IQR''') is a measure of [[statistical dispersion]], which is the spread of the data.<ref name=":1">{{Cite book|last=Dekking|first=Frederik Michel|url=http://link.springer.com/10.1007/1-84628-168-7|title=A Modern Introduction to Probability and Statistics|last2=Kraaikamp|first2=Cornelis|last3=Lopuhaä|first3=Hen Paul|last4=Meester|first4=Ludolf Erwin|date=2005|publisher=Springer London|isbn=978-1-85233-896-1|series=Springer Texts in Statistics|location=London|doi=10.1007/1-84628-168-7}}</ref> The IQR may also be called the '''midspread''', '''middle 50%''', '''fourth spread''', or L'''‑spread.''' It is defined as the difference between the 75th and 25th [[percentiles]] of the data.<ref name="Upton" /><ref name="ZK" /><ref>{{Cite book|last=Ross|first=Sheldon|title=Introductory Statistics|publisher=Elsevier|year=2010|isbn=978-0-12-374388-6|location=Burlington, MA|pages=103–104}}</ref> To calculate the IQR, the data set is divided into [[quartile]]s, or four rank-ordered even parts via linear interpolation.<ref name=":1" /> These quartiles are denoted by Q<sub>1</sub> (also called the lower quartile), ''Q''<sub>2</sub> (the [[median]]), and ''Q''<sub>3</sub> (also called the upper quartile). The lower quartile corresponds with the 25th percentile and the upper quartile corresponds with the 75th percentile, so IQR = ''Q''<sub>3</sub> − ''Q''<sub>1</sub><ref name=":1" /><sub>.</sub>',
2 => 'The IQR is an example of a [[trimmed estimator]], defined as the 25% trimmed [[Range (statistics)|range]], which enhances the accuracy of dataset statistics by dropping lower contribution, outlying points.<ref name=":2">{{Cite book|last=Kaltenbach|first=Hans-Michael|url=https://www.worldcat.org/oclc/763157853|title=A concise guide to statistics|date=2012|publisher=Springer|isbn=978-3-642-23502-3|location=Heidelberg|oclc=763157853}}</ref> It is also used as a [[Robust measures of scale|robust measure of scale]]<ref name=":2" /> It can be clearly visualized by the box on a [[box plot]].<ref name=":1" />'
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Parsed HTML source of the new revision (new_html) | '<div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Measure of statistical dispersion</div>
<style data-mw-deduplicate="TemplateStyles:r1033289096">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}</style><div role="note" class="hatnote navigation-not-searchable">"IQR" redirects here. For other uses, see <a href="/info/en/?search=IQR_(disambiguation)" class="mw-disambig" title="IQR (disambiguation)">IQR (disambiguation)</a>.</div>
<figure typeof="mw:File/Thumb"><a href="/info/en/?search=File:Boxplot_vs_PDF.svg" class="mw-file-description"><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Boxplot_vs_PDF.svg/250px-Boxplot_vs_PDF.svg.png" decoding="async" width="250" height="273" class="mw-file-element" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Boxplot_vs_PDF.svg/375px-Boxplot_vs_PDF.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Boxplot_vs_PDF.svg/500px-Boxplot_vs_PDF.svg.png 2x" data-file-width="598" data-file-height="652" /></a><figcaption><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/info/en/?search=File:Skibidi_Toilet_fan-art.jpg" class="mw-file-description"><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Skibidi_Toilet_fan-art.jpg/220px-Skibidi_Toilet_fan-art.jpg" decoding="async" width="220" height="153" class="mw-file-element" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Skibidi_Toilet_fan-art.jpg/330px-Skibidi_Toilet_fan-art.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/Skibidi_Toilet_fan-art.jpg/440px-Skibidi_Toilet_fan-art.jpg 2x" data-file-width="3430" data-file-height="2388" /></a><figcaption>sigma rizz 999</figcaption></figure>Skibidi Rizz 999 graph</figcaption></figure>
<p>Why am I sigma? 6 reasons 999
</p>
<ol><li><b>Self-Reliance</b>:
<ul><li>Sigmas can function well in social groups if needed, but they also enjoy spending time alone.</li>
<li>They don’t depend on others and are comfortable being their own best friend.</li></ul></li>
<li><b>Emotional Independence</b>:
<ul><li>Sigmas don’t rely on external validation for happiness or completeness.</li>
<li>They take full responsibility for their own feelings.</li></ul></li>
<li><b>Authenticity</b>:
<ul><li>Authenticity is a common trait among sigmas.</li>
<li>They are genuine, comfortable in their own skin, and don’t pretend to be someone they’re not.</li></ul></li>
<li><b>Quiet Confidence</b>:
<ul><li>Sigmas may not appear extremely confident like alphas, but they have strong self-esteem.</li>
<li>Their quiet demeanor often hides their inner confidence.</li></ul></li>
<li><b>Success-Oriented</b>:
<ul><li>Sigmas tend to be successful because of their self-reliance, ambition, and determination.</li>
<li>They know what they want and pursue it relentlessly.</li></ul></li>
<li><b>Great Listeners</b>:
<ul><li>Their introverted nature allows them to listen attentively to others.</li></ul></li></ol>
<p>Remember that being a sigma is not better or worse than other personality types—it’s simply a unique combination of traits. Embrace your individuality and continue to grow!
</p><p>The IQR is an example of a <a href="/info/en/?search=Trimmed_estimator" title="Trimmed estimator">trimmed estimator</a>, defined as the 25% trimmed <a href="/info/en/?search=Range_(statistics)" title="Range (statistics)">range</a>, which enhances the accuracy of dataset statistics by dropping lower contribution, outlying points.<sup id="cite_ref-:2_1-0" class="reference"><a href="#cite_note-:2-1">[1]</a></sup> It is also used as a <a href="/info/en/?search=Robust_measures_of_scale" title="Robust measures of scale">robust measure of scale</a><sup id="cite_ref-:2_1-1" class="reference"><a href="#cite_note-:2-1">[1]</a></sup> It can be clearly visualized by the box on a <a href="/info/en/?search=Box_plot" title="Box plot">box plot</a>.<sup id="cite_ref-:1_2-0" class="reference"><a href="#cite_note-:1-2">[2]</a></sup>
</p>
<div id="toc" class="toc" role="navigation" aria-labelledby="mw-toc-heading"><input type="checkbox" role="button" id="toctogglecheckbox" class="toctogglecheckbox" style="display:none" /><div class="toctitle" lang="en" dir="ltr"><h2 id="mw-toc-heading">Contents</h2><span class="toctogglespan"><label class="toctogglelabel" for="toctogglecheckbox"></label></span></div>
<ul>
<li class="toclevel-1 tocsection-1"><a href="#Use"><span class="tocnumber">1</span> <span class="toctext">Use</span></a></li>
<li class="toclevel-1 tocsection-2"><a href="#Algorithm"><span class="tocnumber">2</span> <span class="toctext">Algorithm</span></a></li>
<li class="toclevel-1 tocsection-3"><a href="#Examples"><span class="tocnumber">3</span> <span class="toctext">Examples</span></a>
<ul>
<li class="toclevel-2 tocsection-4"><a href="#Data_set_in_a_table"><span class="tocnumber">3.1</span> <span class="toctext">Data set in a table</span></a></li>
<li class="toclevel-2 tocsection-5"><a href="#Data_set_in_a_plain-text_box_plot"><span class="tocnumber">3.2</span> <span class="toctext">Data set in a plain-text box plot</span></a></li>
</ul>
</li>
<li class="toclevel-1 tocsection-6"><a href="#Distributions"><span class="tocnumber">4</span> <span class="toctext">Distributions</span></a>
<ul>
<li class="toclevel-2 tocsection-7"><a href="#Interquartile_range_test_for_normality_of_distribution"><span class="tocnumber">4.1</span> <span class="toctext">Interquartile range test for normality of distribution</span></a></li>
</ul>
</li>
<li class="toclevel-1 tocsection-8"><a href="#Outliers"><span class="tocnumber">5</span> <span class="toctext">Outliers</span></a></li>
<li class="toclevel-1 tocsection-9"><a href="#See_also"><span class="tocnumber">6</span> <span class="toctext">See also</span></a></li>
<li class="toclevel-1 tocsection-10"><a href="#References"><span class="tocnumber">7</span> <span class="toctext">References</span></a></li>
<li class="toclevel-1 tocsection-11"><a href="#External_links"><span class="tocnumber">8</span> <span class="toctext">External links</span></a></li>
</ul>
</div>
<h2><span class="mw-headline" id="Use">Use</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="https://en.wikipedia.org/?title=Interquartile_range&action=edit&section=1" title="Edit section: Use"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></h2>
<p>Unlike total <a href="/info/en/?search=Range_(statistics)" title="Range (statistics)">range</a>, the interquartile range has a <a href="/info/en/?search=Breakdown_point" class="mw-redirect" title="Breakdown point">breakdown point</a> of 25%<sup id="cite_ref-3" class="reference"><a href="#cite_note-3">[3]</a></sup> and is thus often preferred to the total range.
</p><p>The IQR is used to build <a href="/info/en/?search=Box_plot" title="Box plot">box plots</a>, simple graphical representations of a <a href="/info/en/?search=Probability_distribution" title="Probability distribution">probability distribution</a>.
</p><p>The IQR is used in businesses as a marker for their <a href="/info/en/?search=Income" title="Income">income</a> rates.
</p><p>For a symmetric distribution (where the median equals the <a href="/info/en/?search=Midhinge" title="Midhinge">midhinge</a>, the average of the first and third quartiles), half the IQR equals the <a href="/info/en/?search=Median_absolute_deviation" title="Median absolute deviation">median absolute deviation</a> (MAD).
</p><p>The <a href="/info/en/?search=Median" title="Median">median</a> is the corresponding measure of <a href="/info/en/?search=Central_tendency" title="Central tendency">central tendency</a>.
</p><p>The IQR can be used to identify <a href="/info/en/?search=Outlier" title="Outlier">outliers</a> (see <a href="#Outliers">below</a>). The IQR also may indicate the <a href="/info/en/?search=Skewness" title="Skewness">skewness</a> of the dataset.<sup id="cite_ref-:1_2-1" class="reference"><a href="#cite_note-:1-2">[2]</a></sup>
</p><p><span class="anchor" id="Quartile_deviation"></span> The quartile deviation or semi-interquartile range is defined as half the IQR.<sup id="cite_ref-Yule_4-0" class="reference"><a href="#cite_note-Yule-4">[4]</a></sup>
</p>
<h2><span class="mw-headline" id="Algorithm">Algorithm</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="https://en.wikipedia.org/?title=Interquartile_range&action=edit&section=2" title="Edit section: Algorithm"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></h2>
<p>The IQR of a set of values is calculated as the difference between the upper and lower quartiles, Q<sub>3</sub> and Q<sub>1</sub>. Each quartile is a median<sup id="cite_ref-:0_5-0" class="reference"><a href="#cite_note-:0-5">[5]</a></sup> calculated as follows.
</p><p>Given an even <i>2n</i> or odd <i>2n+1</i> number of values
</p>
<dl><dd><i>first quartile Q<sub>1</sub></i> = median of the <i>n</i> smallest values</dd>
<dd><i>third quartile Q<sub>3</sub></i> = median of the <i>n</i> largest values<sup id="cite_ref-:0_5-1" class="reference"><a href="#cite_note-:0-5">[5]</a></sup></dd></dl>
<p>The <i>second quartile Q<sub>2</sub></i> is the same as the ordinary median.<sup id="cite_ref-:0_5-2" class="reference"><a href="#cite_note-:0-5">[5]</a></sup>
</p>
<h2><span class="mw-headline" id="Examples">Examples</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="https://en.wikipedia.org/?title=Interquartile_range&action=edit&section=3" title="Edit section: Examples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></h2>
<h3><span class="mw-headline" id="Data_set_in_a_table">Data set in a table</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="https://en.wikipedia.org/?title=Interquartile_range&action=edit&section=4" title="Edit section: Data set in a table"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></h3>
<p>The following table has 13 rows, and follows the rules for the odd number of entries.
</p>
<table class="wikitable" style="text-align:center;">
<tbody><tr>
<th width="40px">i
</th>
<th width="40px">x[i]
</th>
<th>Median
</th>
<th>Quartile
</th></tr>
<tr>
<td>1
</td>
<td>7
</td>
<td rowspan="14">Q<sub>2</sub>=87<br /> (median of whole table)
</td>
<td rowspan="6">Q<sub>1</sub>=31<br /> (median of lower half, from row 1 to 6)
</td></tr>
<tr>
<td>2
</td>
<td>7
</td></tr>
<tr>
<td>3
</td>
<td>31
</td></tr>
<tr>
<td>4
</td>
<td>31
</td></tr>
<tr>
<td>5
</td>
<td>47
</td></tr>
<tr>
<td>6
</td>
<td>75
</td></tr>
<tr>
<td>7
</td>
<td>87
</td>
<td>
</td></tr>
<tr>
<td>8
</td>
<td>115
</td>
<td rowspan="6">Q<sub>3</sub>=119<br /> (median of upper half, from row 8 to 13)
</td></tr>
<tr>
<td>9
</td>
<td>116
</td></tr>
<tr>
<td>10
</td>
<td>119
</td></tr>
<tr>
<td>11
</td>
<td>119
</td></tr>
<tr>
<td>12
</td>
<td>155
</td></tr>
<tr>
<td>13
</td>
<td>177
</td></tr></tbody></table>
<p>For the data in this table the interquartile range is IQR = Q<sub>3</sub> − Q<sub>1</sub> = 119 - 31 = 88.
</p>
<h3><span class="mw-headline" id="Data_set_in_a_plain-text_box_plot">Data set in a plain-text box plot</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="https://en.wikipedia.org/?title=Interquartile_range&action=edit&section=5" title="Edit section: Data set in a plain-text box plot"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></h3>
<pre style="font-family:monospace">
+−−−−−+−+
* |−−−−−−−−−−−| | |−−−−−−−−−−−|
+−−−−−+−+
+−−−+−−−+−−−+−−−+−−−+−−−+−−−+−−−+−−−+−−−+−−−+−−−+ number line
0 1 2 3 4 5 6 7 8 9 10 11 12
</pre>
<p>For the data set in this <a href="/info/en/?search=Box_plot" title="Box plot">box plot</a>:
</p>
<ul><li>Lower (first) quartile <i>Q</i><sub>1</sub> = 7</li>
<li>Median (second quartile) <i>Q</i><sub>2</sub> = 8.5</li>
<li>Upper (third) quartile <i>Q</i><sub>3</sub> = 9</li>
<li>Interquartile range, IQR = <i>Q</i><sub>3</sub> - <i>Q</i><sub>1</sub> = 2</li>
<li>Lower 1.5*IQR whisker = <i>Q</i><sub>1</sub> - 1.5 * IQR = 7 - 3 = 4. (If there is no data point at 4, then the lowest point greater than 4.)</li>
<li>Upper 1.5*IQR whisker = <i>Q</i><sub>3</sub> + 1.5 * IQR = 9 + 3 = 12. (If there is no data point at 12, then the highest point less than 12.)</li>
<li>Pattern of latter two bullet points: If there are no data points at the true quartiles, use data points slightly "inland" (closer to the median) from the actual quartiles.</li></ul>
<p>This means the 1.5*IQR whiskers can be uneven in lengths. The median, minimum, maximum, and the first and third quartile constitute the <a href="/info/en/?search=Five-number_summary" title="Five-number summary">Five-number summary</a>.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6">[6]</a></sup>
</p>
<h2><span class="mw-headline" id="Distributions">Distributions</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="https://en.wikipedia.org/?title=Interquartile_range&action=edit&section=6" title="Edit section: Distributions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></h2>
<p>The interquartile range of a continuous distribution can be calculated by integrating the <a href="/info/en/?search=Probability_density_function" title="Probability density function">probability density function</a> (which yields the <a href="/info/en/?search=Cumulative_distribution_function" title="Cumulative distribution function">cumulative distribution function</a>—any other means of calculating the CDF will also work). The lower quartile, <i>Q</i><sub>1</sub>, is a number such that integral of the PDF from -∞ to <i>Q</i><sub>1</sub> equals 0.25, while the upper quartile, <i>Q</i><sub>3</sub>, is such a number that the integral from -∞ to <i>Q</i><sub>3</sub> equals 0.75; in terms of the CDF, the quartiles can be defined as follows:
</p>
<dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q_{1}={\text{CDF}}^{-1}(0.25),}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>Q</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
<mo>=</mo>
<msup>
<mrow class="MJX-TeXAtom-ORD">
<mtext>CDF</mtext>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>−<!-- − --></mo>
<mn>1</mn>
</mrow>
</msup>
<mo stretchy="false">(</mo>
<mn>0.25</mn>
<mo stretchy="false">)</mo>
<mo>,</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle Q_{1}={\text{CDF}}^{-1}(0.25),}</annotation>
</semantics>
</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c216c8e09bcf02cbb53d2e1c36e4606112f2a2e" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.886ex; height:3.176ex;" alt="{\displaystyle Q_{1}={\text{CDF}}^{-1}(0.25),}"></span></dd></dl>
<dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q_{3}={\text{CDF}}^{-1}(0.75),}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>Q</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>3</mn>
</mrow>
</msub>
<mo>=</mo>
<msup>
<mrow class="MJX-TeXAtom-ORD">
<mtext>CDF</mtext>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>−<!-- − --></mo>
<mn>1</mn>
</mrow>
</msup>
<mo stretchy="false">(</mo>
<mn>0.75</mn>
<mo stretchy="false">)</mo>
<mo>,</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle Q_{3}={\text{CDF}}^{-1}(0.75),}</annotation>
</semantics>
</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe74613075ffde70c61311d994e59de085bb8411" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.886ex; height:3.176ex;" alt="{\displaystyle Q_{3}={\text{CDF}}^{-1}(0.75),}"></span></dd></dl>
<p>where CDF<sup>−1</sup> is the <a href="/info/en/?search=Quantile_function" title="Quantile function">quantile function</a>.
</p><p>The interquartile range and median of some common distributions are shown below
</p>
<table class="wikitable">
<tbody><tr>
<th>Distribution
</th>
<th>Median
</th>
<th>IQR
</th></tr>
<tr>
<td><a href="/info/en/?search=Normal_distribution" title="Normal distribution">Normal</a>
</td>
<td>μ
</td>
<td>2 Φ<sup>−1</sup>(0.75)σ ≈ 1.349σ ≈ (27/20)σ
</td></tr>
<tr>
<td><a href="/info/en/?search=Laplace_distribution" title="Laplace distribution">Laplace</a>
</td>
<td>μ
</td>
<td>2<i>b</i> ln(2) ≈ 1.386<i>b</i>
</td></tr>
<tr>
<td><a href="/info/en/?search=Cauchy_distribution" title="Cauchy distribution">Cauchy</a>
</td>
<td>μ
</td>
<td>2γ
</td></tr></tbody></table>
<h3><span class="mw-headline" id="Interquartile_range_test_for_normality_of_distribution">Interquartile range test for normality of distribution</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="https://en.wikipedia.org/?title=Interquartile_range&action=edit&section=7" title="Edit section: Interquartile range test for normality of distribution"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></h3>
<p>The IQR, <a href="/info/en/?search=Mean" title="Mean">mean</a>, and <a href="/info/en/?search=Standard_deviation" title="Standard deviation">standard deviation</a> of a population <i>P</i> can be used in a simple test of whether or not <i>P</i> is <a href="/info/en/?search=Normal_distribution" title="Normal distribution">normally distributed</a>, or Gaussian. If <i>P</i> is normally distributed, then the <a href="/info/en/?search=Standard_score" title="Standard score">standard score</a> of the first quartile, <i>z</i><sub>1</sub>, is −0.67, and the standard score of the third quartile, <i>z</i><sub>3</sub>, is +0.67. Given <i>mean</i> = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\bar {P}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>P</mi>
<mo stretchy="false">¯<!-- ¯ --></mo>
</mover>
</mrow>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\bar {P}}}</annotation>
</semantics>
</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9d1fdaf8f50ca1bfe522c83b892dd55f87659fe" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.812ex; height:2.509ex;" alt="{\displaystyle {\bar {P}}}"></span> and <i>standard deviation</i> = σ for <i>P</i>, if <i>P</i> is normally distributed, the first quartile
</p>
<dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q_{1}=(\sigma \,z_{1})+{\bar {P}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>Q</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
<mo>=</mo>
<mo stretchy="false">(</mo>
<mi>σ<!-- σ --></mi>
<mspace width="thinmathspace" />
<msub>
<mi>z</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>P</mi>
<mo stretchy="false">¯<!-- ¯ --></mo>
</mover>
</mrow>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle Q_{1}=(\sigma \,z_{1})+{\bar {P}}}</annotation>
</semantics>
</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4ac86347369fbae9eb05b896c5a2fd7394630eee" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.305ex; height:3.009ex;" alt="{\displaystyle Q_{1}=(\sigma \,z_{1})+{\bar {P}}}"></span></dd></dl>
<p>and the third quartile
</p>
<dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q_{3}=(\sigma \,z_{3})+{\bar {P}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>Q</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>3</mn>
</mrow>
</msub>
<mo>=</mo>
<mo stretchy="false">(</mo>
<mi>σ<!-- σ --></mi>
<mspace width="thinmathspace" />
<msub>
<mi>z</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>3</mn>
</mrow>
</msub>
<mo stretchy="false">)</mo>
<mo>+</mo>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>P</mi>
<mo stretchy="false">¯<!-- ¯ --></mo>
</mover>
</mrow>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle Q_{3}=(\sigma \,z_{3})+{\bar {P}}}</annotation>
</semantics>
</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81f4c0fcee75fd8c972cef6767619499d8374046" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.305ex; height:3.009ex;" alt="{\displaystyle Q_{3}=(\sigma \,z_{3})+{\bar {P}}}"></span></dd></dl>
<p>If the actual values of the first or third quartiles differ substantially<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/info/en/?search=Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="The text near this tag may need clarification or removal of jargon. (December 2012)">clarification needed</span></a></i>]</sup> from the calculated values, <i>P</i> is not normally distributed. However, a normal distribution can be trivially perturbed to maintain its Q1 and Q2 std. scores at 0.67 and −0.67 and not be normally distributed (so the above test would produce a false positive). A better test of normality, such as <a href="/info/en/?search=Q%E2%80%93Q_plot" title="Q–Q plot">Q–Q plot</a> would be indicated here.
</p>
<h2><span class="mw-headline" id="Outliers">Outliers</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="https://en.wikipedia.org/?title=Interquartile_range&action=edit&section=8" title="Edit section: Outliers"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></h2>
<figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/info/en/?search=File:Box-Plot_mit_Interquartilsabstand.png" class="mw-file-description"><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/2/2b/Box-Plot_mit_Interquartilsabstand.png/220px-Box-Plot_mit_Interquartilsabstand.png" decoding="async" width="220" height="165" class="mw-file-element" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/2/2b/Box-Plot_mit_Interquartilsabstand.png/330px-Box-Plot_mit_Interquartilsabstand.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2b/Box-Plot_mit_Interquartilsabstand.png/440px-Box-Plot_mit_Interquartilsabstand.png 2x" data-file-width="715" data-file-height="536" /></a><figcaption><a href="/info/en/?search=Box-and-whisker_plot" class="mw-redirect" title="Box-and-whisker plot">Box-and-whisker plot</a> with four mild outliers and one extreme outlier. In this chart, outliers are defined as mild above Q3 + 1.5 IQR and extreme above Q3 + 3 IQR.</figcaption></figure>
<p>The interquartile range is often used to find <a href="/info/en/?search=Outlier" title="Outlier">outliers</a> in data. Outliers here are defined as observations that fall below Q1 − 1.5 IQR or above Q3 + 1.5 IQR. In a boxplot, the highest and lowest occurring value within this limit are indicated by <i>whiskers</i> of the box (frequently with an additional bar at the end of the whisker) and any outliers as individual points.
</p>
<h2><span class="mw-headline" id="See_also">See also</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="https://en.wikipedia.org/?title=Interquartile_range&action=edit&section=9" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></h2>
<ul><li><a href="/info/en/?search=Interdecile_range" title="Interdecile range">Interdecile range</a> – Statistical measure</li>
<li><a href="/info/en/?search=Midhinge" title="Midhinge">Midhinge</a> – average of the first and third quartiles<span style="display:none" class="category-wikidata-fallback-annotation">Pages displaying wikidata descriptions as a fallback</span></li>
<li><a href="/info/en/?search=Probable_error" title="Probable error">Probable error</a></li>
<li><a href="/info/en/?search=Robust_measures_of_scale" title="Robust measures of scale">Robust measures of scale</a> – Statistical indicators of the deviation of a sample</li></ul>
<h2><span class="mw-headline" id="References">References</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="https://en.wikipedia.org/?title=Interquartile_range&action=edit&section=10" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></h2>
<style data-mw-deduplicate="TemplateStyles:r1217336898">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist">
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<li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite id="CITEREFRousseeuwCroux1992" class="citation news cs1">Rousseeuw, Peter J.; Croux, Christophe (1992). Y. Dodge (ed.). <a class="external text" href="https://feb.kuleuven.be/public/u0017833/PDF-FILES/l11992.pdf">"Explicit Scale Estimators with High Breakdown Point"</a> <span class="cs1-format">(PDF)</span>. <i>L1-Statistical Analysis and Related Methods</i>. Amsterdam: North-Holland. pp. 77–92.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=L1-Statistical+Analysis+and+Related+Methods&rft.atitle=Explicit+Scale+Estimators+with+High+Breakdown+Point&rft.pages=77-92&rft.date=1992&rft.aulast=Rousseeuw&rft.aufirst=Peter+J.&rft.au=Croux%2C+Christophe&rft_id=https%3A%2F%2Ffeb.kuleuven.be%2Fpublic%2Fu0017833%2FPDF-FILES%2Fl11992.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInterquartile+range" class="Z3988"></span></span>
</li>
<li id="cite_note-Yule-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-Yule_4-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite id="CITEREFYule1911" class="citation book cs1">Yule, G. Udny (1911). <a class="external text" href="https://archive.org/details/in.ernet.dli.2015.223539"><i>An Introduction to the Theory of Statistics</i></a>. Charles Griffin and Company. pp. <a class="external text" href="https://archive.org/details/in.ernet.dli.2015.223539/page/n170">147</a>–148.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=An+Introduction+to+the+Theory+of+Statistics&rft.pages=147-148&rft.pub=Charles+Griffin+and+Company&rft.date=1911&rft.aulast=Yule&rft.aufirst=G.+Udny&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fin.ernet.dli.2015.223539&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInterquartile+range" class="Z3988"></span></span>
</li>
<li id="cite_note-:0-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_5-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:0_5-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite id="CITEREFBertil.1988" class="citation book cs1">Bertil., Westergren (1988). <i>Beta [beta] mathematics handbook : concepts, theorems, methods, algorithms, formulas, graphs, tables</i>. <a href="/info/en/?search=Studentlitteratur" title="Studentlitteratur">Studentlitteratur</a>. p. 348. <a href="/info/en/?search=ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/info/en/?search=Special:BookSources/9144250517" title="Special:BookSources/9144250517"><bdi>9144250517</bdi></a>. <a href="/info/en/?search=OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a class="external text" href="https://www.worldcat.org/oclc/18454776">18454776</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Beta+%5Bbeta%5D+mathematics+handbook+%3A+concepts%2C+theorems%2C+methods%2C+algorithms%2C+formulas%2C+graphs%2C+tables&rft.pages=348&rft.pub=Studentlitteratur&rft.date=1988&rft_id=info%3Aoclcnum%2F18454776&rft.isbn=9144250517&rft.aulast=Bertil.&rft.aufirst=Westergren&rfr_id=info%3Asid%2Fen.wikipedia.org%3AInterquartile+range" class="Z3988"></span></span>
</li>
<li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text">Dekking, Kraaikamp, Lopuhaä & Meester, pp. 235–237</span>
</li>
</ol></div>
<p><span class="error mw-ext-cite-error" lang="en" dir="ltr">Cite error: A <a href="/info/en/?search=Help:Footnotes#WP:LDR" title="Help:Footnotes">list-defined reference</a> named "Upton" is not used in the content (see the <a href="/info/en/?search=Help:Cite_errors/Cite_error_references_missing_key" title="Help:Cite errors/Cite error references missing key">help page</a>).</span><br />
</p>
<span class="error mw-ext-cite-error" lang="en" dir="ltr">Cite error: A <a href="/info/en/?search=Help:Footnotes#WP:LDR" title="Help:Footnotes">list-defined reference</a> named "ZK" is not used in the content (see the <a href="/info/en/?search=Help:Cite_errors/Cite_error_references_missing_key" title="Help:Cite errors/Cite error references missing key">help page</a>).</span></div>
<h2><span class="mw-headline" id="External_links">External links</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="https://en.wikipedia.org/?title=Interquartile_range&action=edit&section=11" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></h2>
<ul><li><span class="noviewer" typeof="mw:File"><a href="/info/en/?search=File:Commons-logo.svg" class="mw-file-description"><img alt="" src="https://upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="https://upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> Media related to <a href="https://commons.wikimedia.org/wiki/Category:Interquartile_range" class="extiw" title="commons:Category:Interquartile range">Interquartile range</a> at Wikimedia Commons</li></ul>
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<ul><li><a href="/info/en/?search=Outline_of_statistics" title="Outline of statistics">Outline</a></li>
<li><a href="/info/en/?search=List_of_statistics_articles" title="List of statistics articles">Index</a></li></ul>
</div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible uncollapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Descriptive_statistics" style="font-size:114%;margin:0 4em"><a href="/info/en/?search=Descriptive_statistics" title="Descriptive statistics">Descriptive statistics</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/info/en/?search=Continuous_probability_distribution" class="mw-redirect" title="Continuous probability distribution">Continuous data</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/info/en/?search=Central_tendency" title="Central tendency">Center</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Mean" title="Mean">Mean</a>
<ul><li><a href="/info/en/?search=Arithmetic_mean" title="Arithmetic mean">Arithmetic</a></li>
<li><a href="/info/en/?search=Arithmetic%E2%80%93geometric_mean" title="Arithmetic–geometric mean">Arithmetic-Geometric</a></li>
<li><a href="/info/en/?search=Cubic_mean" title="Cubic mean">Cubic</a></li>
<li><a href="/info/en/?search=Generalized_mean" title="Generalized mean">Generalized/power</a></li>
<li><a href="/info/en/?search=Geometric_mean" title="Geometric mean">Geometric</a></li>
<li><a href="/info/en/?search=Harmonic_mean" title="Harmonic mean">Harmonic</a></li>
<li><a href="/info/en/?search=Heronian_mean" title="Heronian mean">Heronian</a></li>
<li><a href="/info/en/?search=Heinz_mean" title="Heinz mean">Heinz</a></li>
<li><a href="/info/en/?search=Lehmer_mean" title="Lehmer mean">Lehmer</a></li></ul></li>
<li><a href="/info/en/?search=Median" title="Median">Median</a></li>
<li><a href="/info/en/?search=Mode_(statistics)" title="Mode (statistics)">Mode</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/info/en/?search=Statistical_dispersion" title="Statistical dispersion">Dispersion</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Average_absolute_deviation" title="Average absolute deviation">Average absolute deviation</a></li>
<li><a href="/info/en/?search=Coefficient_of_variation" title="Coefficient of variation">Coefficient of variation</a></li>
<li><a class="mw-selflink selflink">Interquartile range</a></li>
<li><a href="/info/en/?search=Percentile" title="Percentile">Percentile</a></li>
<li><a href="/info/en/?search=Range_(statistics)" title="Range (statistics)">Range</a></li>
<li><a href="/info/en/?search=Standard_deviation" title="Standard deviation">Standard deviation</a></li>
<li><a href="/info/en/?search=Variance#Sample_variance" title="Variance">Variance</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/info/en/?search=Shape_of_the_distribution" class="mw-redirect" title="Shape of the distribution">Shape</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Central_limit_theorem" title="Central limit theorem">Central limit theorem</a></li>
<li><a href="/info/en/?search=Moment_(mathematics)" title="Moment (mathematics)">Moments</a>
<ul><li><a href="/info/en/?search=Kurtosis" title="Kurtosis">Kurtosis</a></li>
<li><a href="/info/en/?search=L-moment" title="L-moment">L-moments</a></li>
<li><a href="/info/en/?search=Skewness" title="Skewness">Skewness</a></li></ul></li></ul>
</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/info/en/?search=Count_data" title="Count data">Count data</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Index_of_dispersion" title="Index of dispersion">Index of dispersion</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em">Summary tables</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Contingency_table" title="Contingency table">Contingency table</a></li>
<li><a href="/info/en/?search=Frequency_distribution" class="mw-redirect" title="Frequency distribution">Frequency distribution</a></li>
<li><a href="/info/en/?search=Grouped_data" title="Grouped data">Grouped data</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/info/en/?search=Correlation_and_dependence" class="mw-redirect" title="Correlation and dependence">Dependence</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Partial_correlation" title="Partial correlation">Partial correlation</a></li>
<li><a href="/info/en/?search=Pearson_correlation_coefficient" title="Pearson correlation coefficient">Pearson product-moment correlation</a></li>
<li><a href="/info/en/?search=Rank_correlation" title="Rank correlation">Rank correlation</a>
<ul><li><a href="/info/en/?search=Kendall_rank_correlation_coefficient" title="Kendall rank correlation coefficient">Kendall's τ</a></li>
<li><a href="/info/en/?search=Spearman%27s_rank_correlation_coefficient" title="Spearman's rank correlation coefficient">Spearman's ρ</a></li></ul></li>
<li><a href="/info/en/?search=Scatter_plot" title="Scatter plot">Scatter plot</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/info/en/?search=Statistical_graphics" title="Statistical graphics">Graphics</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Bar_chart" title="Bar chart">Bar chart</a></li>
<li><a href="/info/en/?search=Biplot" title="Biplot">Biplot</a></li>
<li><a href="/info/en/?search=Box_plot" title="Box plot">Box plot</a></li>
<li><a href="/info/en/?search=Control_chart" title="Control chart">Control chart</a></li>
<li><a href="/info/en/?search=Correlogram" title="Correlogram">Correlogram</a></li>
<li><a href="/info/en/?search=Fan_chart_(statistics)" title="Fan chart (statistics)">Fan chart</a></li>
<li><a href="/info/en/?search=Forest_plot" title="Forest plot">Forest plot</a></li>
<li><a href="/info/en/?search=Histogram" title="Histogram">Histogram</a></li>
<li><a href="/info/en/?search=Pie_chart" title="Pie chart">Pie chart</a></li>
<li><a href="/info/en/?search=Q%E2%80%93Q_plot" title="Q–Q plot">Q–Q plot</a></li>
<li><a href="/info/en/?search=Radar_chart" title="Radar chart">Radar chart</a></li>
<li><a href="/info/en/?search=Run_chart" title="Run chart">Run chart</a></li>
<li><a href="/info/en/?search=Scatter_plot" title="Scatter plot">Scatter plot</a></li>
<li><a href="/info/en/?search=Stem-and-leaf_display" title="Stem-and-leaf display">Stem-and-leaf display</a></li>
<li><a href="/info/en/?search=Violin_plot" title="Violin plot">Violin plot</a></li></ul>
</div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Data_collection" style="font-size:114%;margin:0 4em"><a href="/info/en/?search=Data_collection" title="Data collection">Data collection</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/info/en/?search=Design_of_experiments" title="Design of experiments">Study design</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Effect_size" title="Effect size">Effect size</a></li>
<li><a href="/info/en/?search=Missing_data" title="Missing data">Missing data</a></li>
<li><a href="/info/en/?search=Optimal_design" class="mw-redirect" title="Optimal design">Optimal design</a></li>
<li><a href="/info/en/?search=Statistical_population" title="Statistical population">Population</a></li>
<li><a href="/info/en/?search=Replication_(statistics)" title="Replication (statistics)">Replication</a></li>
<li><a href="/info/en/?search=Sample_size_determination" title="Sample size determination">Sample size determination</a></li>
<li><a href="/info/en/?search=Statistic" title="Statistic">Statistic</a></li>
<li><a href="/info/en/?search=Statistical_power" class="mw-redirect" title="Statistical power">Statistical power</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/info/en/?search=Survey_methodology" title="Survey methodology">Survey methodology</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Sampling_(statistics)" title="Sampling (statistics)">Sampling</a>
<ul><li><a href="/info/en/?search=Cluster_sampling" title="Cluster sampling">Cluster</a></li>
<li><a href="/info/en/?search=Stratified_sampling" title="Stratified sampling">Stratified</a></li></ul></li>
<li><a href="/info/en/?search=Opinion_poll" title="Opinion poll">Opinion poll</a></li>
<li><a href="/info/en/?search=Questionnaire" title="Questionnaire">Questionnaire</a></li>
<li><a href="/info/en/?search=Standard_error" title="Standard error">Standard error</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/info/en/?search=Experiment" title="Experiment">Controlled experiments</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Blocking_(statistics)" title="Blocking (statistics)">Blocking</a></li>
<li><a href="/info/en/?search=Factorial_experiment" title="Factorial experiment">Factorial experiment</a></li>
<li><a href="/info/en/?search=Interaction_(statistics)" title="Interaction (statistics)">Interaction</a></li>
<li><a href="/info/en/?search=Random_assignment" title="Random assignment">Random assignment</a></li>
<li><a href="/info/en/?search=Randomized_controlled_trial" title="Randomized controlled trial">Randomized controlled trial</a></li>
<li><a href="/info/en/?search=Randomized_experiment" title="Randomized experiment">Randomized experiment</a></li>
<li><a href="/info/en/?search=Scientific_control" title="Scientific control">Scientific control</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em">Adaptive designs</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Adaptive_clinical_trial" class="mw-redirect" title="Adaptive clinical trial">Adaptive clinical trial</a></li>
<li><a href="/info/en/?search=Stochastic_approximation" title="Stochastic approximation">Stochastic approximation</a></li>
<li><a href="/info/en/?search=Up-and-Down_Designs" class="mw-redirect" title="Up-and-Down Designs">Up-and-down designs</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/info/en/?search=Observational_study" title="Observational study">Observational studies</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Cohort_study" title="Cohort study">Cohort study</a></li>
<li><a href="/info/en/?search=Cross-sectional_study" title="Cross-sectional study">Cross-sectional study</a></li>
<li><a href="/info/en/?search=Natural_experiment" title="Natural experiment">Natural experiment</a></li>
<li><a href="/info/en/?search=Quasi-experiment" title="Quasi-experiment">Quasi-experiment</a></li></ul>
</div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Statistical_inference" style="font-size:114%;margin:0 4em"><a href="/info/en/?search=Statistical_inference" title="Statistical inference">Statistical inference</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/info/en/?search=Statistical_theory" title="Statistical theory">Statistical theory</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Population_(statistics)" class="mw-redirect" title="Population (statistics)">Population</a></li>
<li><a href="/info/en/?search=Statistic" title="Statistic">Statistic</a></li>
<li><a href="/info/en/?search=Probability_distribution" title="Probability distribution">Probability distribution</a></li>
<li><a href="/info/en/?search=Sampling_distribution" title="Sampling distribution">Sampling distribution</a>
<ul><li><a href="/info/en/?search=Order_statistic" title="Order statistic">Order statistic</a></li></ul></li>
<li><a href="/info/en/?search=Empirical_distribution_function" title="Empirical distribution function">Empirical distribution</a>
<ul><li><a href="/info/en/?search=Density_estimation" title="Density estimation">Density estimation</a></li></ul></li>
<li><a href="/info/en/?search=Statistical_model" title="Statistical model">Statistical model</a>
<ul><li><a href="/info/en/?search=Model_specification" class="mw-redirect" title="Model specification">Model specification</a></li>
<li><a href="/info/en/?search=Lp_space" title="Lp space">L<sup><i>p</i></sup> space</a></li></ul></li>
<li><a href="/info/en/?search=Statistical_parameter" title="Statistical parameter">Parameter</a>
<ul><li><a href="/info/en/?search=Location_parameter" title="Location parameter">location</a></li>
<li><a href="/info/en/?search=Scale_parameter" title="Scale parameter">scale</a></li>
<li><a href="/info/en/?search=Shape_parameter" title="Shape parameter">shape</a></li></ul></li>
<li><a href="/info/en/?search=Parametric_statistics" title="Parametric statistics">Parametric family</a>
<ul><li><a href="/info/en/?search=Likelihood_function" title="Likelihood function">Likelihood</a> <a href="/info/en/?search=Monotone_likelihood_ratio" title="Monotone likelihood ratio"><span style="font-size:85%;">(monotone)</span></a></li>
<li><a href="/info/en/?search=Location%E2%80%93scale_family" title="Location–scale family">Location–scale family</a></li>
<li><a href="/info/en/?search=Exponential_family" title="Exponential family">Exponential family</a></li></ul></li>
<li><a href="/info/en/?search=Completeness_(statistics)" title="Completeness (statistics)">Completeness</a></li>
<li><a href="/info/en/?search=Sufficient_statistic" title="Sufficient statistic">Sufficiency</a></li>
<li><a href="/info/en/?search=Plug-in_principle" class="mw-redirect" title="Plug-in principle">Statistical functional</a>
<ul><li><a href="/info/en/?search=Bootstrapping_(statistics)" title="Bootstrapping (statistics)">Bootstrap</a></li>
<li><a href="/info/en/?search=U-statistic" title="U-statistic">U</a></li>
<li><a href="/info/en/?search=V-statistic" title="V-statistic">V</a></li></ul></li>
<li><a href="/info/en/?search=Optimal_decision" title="Optimal decision">Optimal decision</a>
<ul><li><a href="/info/en/?search=Loss_function" title="Loss function">loss function</a></li></ul></li>
<li><a href="/info/en/?search=Efficiency_(statistics)" title="Efficiency (statistics)">Efficiency</a></li>
<li><a href="/info/en/?search=Statistical_distance" title="Statistical distance">Statistical distance</a>
<ul><li><a href="/info/en/?search=Divergence_(statistics)" title="Divergence (statistics)">divergence</a></li></ul></li>
<li><a href="/info/en/?search=Asymptotic_theory_(statistics)" title="Asymptotic theory (statistics)">Asymptotics</a></li>
<li><a href="/info/en/?search=Robust_statistics" title="Robust statistics">Robustness</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/info/en/?search=Frequentist_inference" title="Frequentist inference">Frequentist inference</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/info/en/?search=Point_estimation" title="Point estimation">Point estimation</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Estimating_equations" title="Estimating equations">Estimating equations</a>
<ul><li><a href="/info/en/?search=Maximum_likelihood" class="mw-redirect" title="Maximum likelihood">Maximum likelihood</a></li>
<li><a href="/info/en/?search=Method_of_moments_(statistics)" title="Method of moments (statistics)">Method of moments</a></li>
<li><a href="/info/en/?search=M-estimator" title="M-estimator">M-estimator</a></li>
<li><a href="/info/en/?search=Minimum_distance_estimation" class="mw-redirect" title="Minimum distance estimation">Minimum distance</a></li></ul></li>
<li><a href="/info/en/?search=Bias_of_an_estimator" title="Bias of an estimator">Unbiased estimators</a>
<ul><li><a href="/info/en/?search=Minimum-variance_unbiased_estimator" title="Minimum-variance unbiased estimator">Mean-unbiased minimum-variance</a>
<ul><li><a href="/info/en/?search=Rao%E2%80%93Blackwell_theorem" title="Rao–Blackwell theorem">Rao–Blackwellization</a></li>
<li><a href="/info/en/?search=Lehmann%E2%80%93Scheff%C3%A9_theorem" title="Lehmann–Scheffé theorem">Lehmann–Scheffé theorem</a></li></ul></li>
<li><a href="/info/en/?search=Median-unbiased_estimator" class="mw-redirect" title="Median-unbiased estimator">Median unbiased</a></li></ul></li>
<li><a href="/info/en/?search=Plug-in_principle" class="mw-redirect" title="Plug-in principle">Plug-in</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/info/en/?search=Interval_estimation" title="Interval estimation">Interval estimation</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Confidence_interval" title="Confidence interval">Confidence interval</a></li>
<li><a href="/info/en/?search=Pivotal_quantity" title="Pivotal quantity">Pivot</a></li>
<li><a href="/info/en/?search=Likelihood_interval" class="mw-redirect" title="Likelihood interval">Likelihood interval</a></li>
<li><a href="/info/en/?search=Prediction_interval" title="Prediction interval">Prediction interval</a></li>
<li><a href="/info/en/?search=Tolerance_interval" title="Tolerance interval">Tolerance interval</a></li>
<li><a href="/info/en/?search=Resampling_(statistics)" title="Resampling (statistics)">Resampling</a>
<ul><li><a href="/info/en/?search=Bootstrapping_(statistics)" title="Bootstrapping (statistics)">Bootstrap</a></li>
<li><a href="/info/en/?search=Jackknife_resampling" title="Jackknife resampling">Jackknife</a></li></ul></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/info/en/?search=Statistical_hypothesis_testing" class="mw-redirect" title="Statistical hypothesis testing">Testing hypotheses</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=One-_and_two-tailed_tests" title="One- and two-tailed tests">1- & 2-tails</a></li>
<li><a href="/info/en/?search=Power_(statistics)" class="mw-redirect" title="Power (statistics)">Power</a>
<ul><li><a href="/info/en/?search=Uniformly_most_powerful_test" title="Uniformly most powerful test">Uniformly most powerful test</a></li></ul></li>
<li><a href="/info/en/?search=Permutation_test" title="Permutation test">Permutation test</a>
<ul><li><a href="/info/en/?search=Randomization_test" class="mw-redirect" title="Randomization test">Randomization test</a></li></ul></li>
<li><a href="/info/en/?search=Multiple_comparisons" class="mw-redirect" title="Multiple comparisons">Multiple comparisons</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/info/en/?search=Parametric_statistics" title="Parametric statistics">Parametric tests</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Likelihood-ratio_test" title="Likelihood-ratio test">Likelihood-ratio</a></li>
<li><a href="/info/en/?search=Score_test" title="Score test">Score/Lagrange multiplier</a></li>
<li><a href="/info/en/?search=Wald_test" title="Wald test">Wald</a></li></ul>
</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/info/en/?search=List_of_statistical_tests" title="List of statistical tests">Specific tests</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Z-test" title="Z-test"><i>Z</i>-test <span style="font-size:85%;">(normal)</span></a></li>
<li><a href="/info/en/?search=Student%27s_t-test" title="Student's t-test">Student's <i>t</i>-test</a></li>
<li><a href="/info/en/?search=F-test" title="F-test"><i>F</i>-test</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/info/en/?search=Goodness_of_fit" title="Goodness of fit">Goodness of fit</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Chi-squared_test" title="Chi-squared test">Chi-squared</a></li>
<li><a href="/info/en/?search=G-test" title="G-test"><i>G</i>-test</a></li>
<li><a href="/info/en/?search=Kolmogorov%E2%80%93Smirnov_test" title="Kolmogorov–Smirnov test">Kolmogorov–Smirnov</a></li>
<li><a href="/info/en/?search=Anderson%E2%80%93Darling_test" title="Anderson–Darling test">Anderson–Darling</a></li>
<li><a href="/info/en/?search=Lilliefors_test" title="Lilliefors test">Lilliefors</a></li>
<li><a href="/info/en/?search=Jarque%E2%80%93Bera_test" title="Jarque–Bera test">Jarque–Bera</a></li>
<li><a href="/info/en/?search=Shapiro%E2%80%93Wilk_test" title="Shapiro–Wilk test">Normality <span style="font-size:85%;">(Shapiro–Wilk)</span></a></li>
<li><a href="/info/en/?search=Likelihood-ratio_test" title="Likelihood-ratio test">Likelihood-ratio test</a></li>
<li><a href="/info/en/?search=Model_selection" title="Model selection">Model selection</a>
<ul><li><a href="/info/en/?search=Cross-validation_(statistics)" title="Cross-validation (statistics)">Cross validation</a></li>
<li><a href="/info/en/?search=Akaike_information_criterion" title="Akaike information criterion">AIC</a></li>
<li><a href="/info/en/?search=Bayesian_information_criterion" title="Bayesian information criterion">BIC</a></li></ul></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/info/en/?search=Rank_statistics" class="mw-redirect" title="Rank statistics">Rank statistics</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Sign_test" title="Sign test">Sign</a>
<ul><li><a href="/info/en/?search=Sample_median" class="mw-redirect" title="Sample median">Sample median</a></li></ul></li>
<li><a href="/info/en/?search=Wilcoxon_signed-rank_test" title="Wilcoxon signed-rank test">Signed rank <span style="font-size:85%;">(Wilcoxon)</span></a>
<ul><li><a href="/info/en/?search=Hodges%E2%80%93Lehmann_estimator" title="Hodges–Lehmann estimator">Hodges–Lehmann estimator</a></li></ul></li>
<li><a href="/info/en/?search=Mann%E2%80%93Whitney_U_test" title="Mann–Whitney U test">Rank sum <span style="font-size:85%;">(Mann–Whitney)</span></a></li>
<li><a href="/info/en/?search=Nonparametric_statistics" title="Nonparametric statistics">Nonparametric</a> <a href="/info/en/?search=Analysis_of_variance" title="Analysis of variance">anova</a>
<ul><li><a href="/info/en/?search=Kruskal%E2%80%93Wallis_test" title="Kruskal–Wallis test">1-way <span style="font-size:85%;">(Kruskal–Wallis)</span></a></li>
<li><a href="/info/en/?search=Friedman_test" title="Friedman test">2-way <span style="font-size:85%;">(Friedman)</span></a></li>
<li><a href="/info/en/?search=Jonckheere%27s_trend_test" title="Jonckheere's trend test">Ordered alternative <span style="font-size:85%;">(Jonckheere–Terpstra)</span></a></li></ul></li>
<li><a href="/info/en/?search=Van_der_Waerden_test" title="Van der Waerden test">Van der Waerden test</a></li></ul>
</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/info/en/?search=Bayesian_inference" title="Bayesian inference">Bayesian inference</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Bayesian_probability" title="Bayesian probability">Bayesian probability</a>
<ul><li><a href="/info/en/?search=Prior_probability" title="Prior probability">prior</a></li>
<li><a href="/info/en/?search=Posterior_probability" title="Posterior probability">posterior</a></li></ul></li>
<li><a href="/info/en/?search=Credible_interval" title="Credible interval">Credible interval</a></li>
<li><a href="/info/en/?search=Bayes_factor" title="Bayes factor">Bayes factor</a></li>
<li><a href="/info/en/?search=Bayes_estimator" title="Bayes estimator">Bayesian estimator</a>
<ul><li><a href="/info/en/?search=Maximum_a_posteriori_estimation" title="Maximum a posteriori estimation">Maximum posterior estimator</a></li></ul></li></ul>
</div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="CorrelationRegression_analysis" style="font-size:114%;margin:0 4em"><div class="hlist"><ul><li><a href="/info/en/?search=Correlation_and_dependence" class="mw-redirect" title="Correlation and dependence">Correlation</a></li><li><a href="/info/en/?search=Regression_analysis" title="Regression analysis">Regression analysis</a></li></ul></div></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/info/en/?search=Correlation_and_dependence" class="mw-redirect" title="Correlation and dependence">Correlation</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Pearson_product-moment_correlation_coefficient" class="mw-redirect" title="Pearson product-moment correlation coefficient">Pearson product-moment</a></li>
<li><a href="/info/en/?search=Partial_correlation" title="Partial correlation">Partial correlation</a></li>
<li><a href="/info/en/?search=Confounding" title="Confounding">Confounding variable</a></li>
<li><a href="/info/en/?search=Coefficient_of_determination" title="Coefficient of determination">Coefficient of determination</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/info/en/?search=Regression_analysis" title="Regression analysis">Regression analysis</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Errors_and_residuals" title="Errors and residuals">Errors and residuals</a></li>
<li><a href="/info/en/?search=Regression_validation" title="Regression validation">Regression validation</a></li>
<li><a href="/info/en/?search=Mixed_model" title="Mixed model">Mixed effects models</a></li>
<li><a href="/info/en/?search=Simultaneous_equations_model" title="Simultaneous equations model">Simultaneous equations models</a></li>
<li><a href="/info/en/?search=Multivariate_adaptive_regression_splines" class="mw-redirect" title="Multivariate adaptive regression splines">Multivariate adaptive regression splines (MARS)</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/info/en/?search=Linear_regression" title="Linear regression">Linear regression</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Simple_linear_regression" title="Simple linear regression">Simple linear regression</a></li>
<li><a href="/info/en/?search=Ordinary_least_squares" title="Ordinary least squares">Ordinary least squares</a></li>
<li><a href="/info/en/?search=General_linear_model" title="General linear model">General linear model</a></li>
<li><a href="/info/en/?search=Bayesian_linear_regression" title="Bayesian linear regression">Bayesian regression</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em">Non-standard predictors</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Nonlinear_regression" title="Nonlinear regression">Nonlinear regression</a></li>
<li><a href="/info/en/?search=Nonparametric_regression" title="Nonparametric regression">Nonparametric</a></li>
<li><a href="/info/en/?search=Semiparametric_regression" title="Semiparametric regression">Semiparametric</a></li>
<li><a href="/info/en/?search=Isotonic_regression" title="Isotonic regression">Isotonic</a></li>
<li><a href="/info/en/?search=Robust_regression" title="Robust regression">Robust</a></li>
<li><a href="/info/en/?search=Heteroscedasticity" class="mw-redirect" title="Heteroscedasticity">Heteroscedasticity</a></li>
<li><a href="/info/en/?search=Homoscedasticity" class="mw-redirect" title="Homoscedasticity">Homoscedasticity</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/info/en/?search=Generalized_linear_model" title="Generalized linear model">Generalized linear model</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Exponential_family" title="Exponential family">Exponential families</a></li>
<li><a href="/info/en/?search=Logistic_regression" title="Logistic regression">Logistic <span style="font-size:85%;">(Bernoulli)</span></a> / <a href="/info/en/?search=Binomial_regression" title="Binomial regression">Binomial</a> / <a href="/info/en/?search=Poisson_regression" title="Poisson regression">Poisson regressions</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/info/en/?search=Partition_of_sums_of_squares" title="Partition of sums of squares">Partition of variance</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Analysis_of_variance" title="Analysis of variance">Analysis of variance (ANOVA, anova)</a></li>
<li><a href="/info/en/?search=Analysis_of_covariance" title="Analysis of covariance">Analysis of covariance</a></li>
<li><a href="/info/en/?search=Multivariate_analysis_of_variance" title="Multivariate analysis of variance">Multivariate ANOVA</a></li>
<li><a href="/info/en/?search=Degrees_of_freedom_(statistics)" title="Degrees of freedom (statistics)">Degrees of freedom</a></li></ul>
</div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Categorical_/_Multivariate_/_Time-series_/_Survival_analysis" style="font-size:114%;margin:0 4em"><a href="/info/en/?search=Categorical_variable" title="Categorical variable">Categorical</a> / <a href="/info/en/?search=Multivariate_statistics" title="Multivariate statistics">Multivariate</a> / <a href="/info/en/?search=Time_series" title="Time series">Time-series</a> / <a href="/info/en/?search=Survival_analysis" title="Survival analysis">Survival analysis</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/info/en/?search=Categorical_variable" title="Categorical variable">Categorical</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Cohen%27s_kappa" title="Cohen's kappa">Cohen's kappa</a></li>
<li><a href="/info/en/?search=Contingency_table" title="Contingency table">Contingency table</a></li>
<li><a href="/info/en/?search=Graphical_model" title="Graphical model">Graphical model</a></li>
<li><a href="/info/en/?search=Poisson_regression" title="Poisson regression">Log-linear model</a></li>
<li><a href="/info/en/?search=McNemar%27s_test" title="McNemar's test">McNemar's test</a></li>
<li><a href="/info/en/?search=Cochran%E2%80%93Mantel%E2%80%93Haenszel_statistics" title="Cochran–Mantel–Haenszel statistics">Cochran–Mantel–Haenszel statistics</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/info/en/?search=Multivariate_statistics" title="Multivariate statistics">Multivariate</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=General_linear_model" title="General linear model">Regression</a></li>
<li><a href="/info/en/?search=Multivariate_analysis_of_variance" title="Multivariate analysis of variance">Manova</a></li>
<li><a href="/info/en/?search=Principal_component_analysis" title="Principal component analysis">Principal components</a></li>
<li><a href="/info/en/?search=Canonical_correlation" title="Canonical correlation">Canonical correlation</a></li>
<li><a href="/info/en/?search=Linear_discriminant_analysis" title="Linear discriminant analysis">Discriminant analysis</a></li>
<li><a href="/info/en/?search=Cluster_analysis" title="Cluster analysis">Cluster analysis</a></li>
<li><a href="/info/en/?search=Statistical_classification" title="Statistical classification">Classification</a></li>
<li><a href="/info/en/?search=Structural_equation_modeling" title="Structural equation modeling">Structural equation model</a>
<ul><li><a href="/info/en/?search=Factor_analysis" title="Factor analysis">Factor analysis</a></li></ul></li>
<li><a href="/info/en/?search=Multivariate_distribution" class="mw-redirect" title="Multivariate distribution">Multivariate distributions</a>
<ul><li><a href="/info/en/?search=Elliptical_distribution" title="Elliptical distribution">Elliptical distributions</a>
<ul><li><a href="/info/en/?search=Multivariate_normal_distribution" title="Multivariate normal distribution">Normal</a></li></ul></li></ul></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/info/en/?search=Time_series" title="Time series">Time-series</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">General</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Decomposition_of_time_series" title="Decomposition of time series">Decomposition</a></li>
<li><a href="/info/en/?search=Trend_estimation" class="mw-redirect" title="Trend estimation">Trend</a></li>
<li><a href="/info/en/?search=Stationary_process" title="Stationary process">Stationarity</a></li>
<li><a href="/info/en/?search=Seasonal_adjustment" title="Seasonal adjustment">Seasonal adjustment</a></li>
<li><a href="/info/en/?search=Exponential_smoothing" title="Exponential smoothing">Exponential smoothing</a></li>
<li><a href="/info/en/?search=Cointegration" title="Cointegration">Cointegration</a></li>
<li><a href="/info/en/?search=Structural_break" title="Structural break">Structural break</a></li>
<li><a href="/info/en/?search=Granger_causality" title="Granger causality">Granger causality</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">Specific tests</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Dickey%E2%80%93Fuller_test" title="Dickey–Fuller test">Dickey–Fuller</a></li>
<li><a href="/info/en/?search=Johansen_test" title="Johansen test">Johansen</a></li>
<li><a href="/info/en/?search=Ljung%E2%80%93Box_test" title="Ljung–Box test">Q-statistic <span style="font-size:85%;">(Ljung–Box)</span></a></li>
<li><a href="/info/en/?search=Durbin%E2%80%93Watson_statistic" title="Durbin–Watson statistic">Durbin–Watson</a></li>
<li><a href="/info/en/?search=Breusch%E2%80%93Godfrey_test" title="Breusch–Godfrey test">Breusch–Godfrey</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/info/en/?search=Time_domain" title="Time domain">Time domain</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Autocorrelation" title="Autocorrelation">Autocorrelation (ACF)</a>
<ul><li><a href="/info/en/?search=Partial_autocorrelation_function" title="Partial autocorrelation function">partial (PACF)</a></li></ul></li>
<li><a href="/info/en/?search=Cross-correlation" title="Cross-correlation">Cross-correlation (XCF)</a></li>
<li><a href="/info/en/?search=Autoregressive%E2%80%93moving-average_model" class="mw-redirect" title="Autoregressive–moving-average model">ARMA model</a></li>
<li><a href="/info/en/?search=Box%E2%80%93Jenkins_method" title="Box–Jenkins method">ARIMA model <span style="font-size:85%;">(Box–Jenkins)</span></a></li>
<li><a href="/info/en/?search=Autoregressive_conditional_heteroskedasticity" title="Autoregressive conditional heteroskedasticity">Autoregressive conditional heteroskedasticity (ARCH)</a></li>
<li><a href="/info/en/?search=Vector_autoregression" title="Vector autoregression">Vector autoregression (VAR)</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/info/en/?search=Frequency_domain" title="Frequency domain">Frequency domain</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Spectral_density_estimation" title="Spectral density estimation">Spectral density estimation</a></li>
<li><a href="/info/en/?search=Fourier_analysis" title="Fourier analysis">Fourier analysis</a></li>
<li><a href="/info/en/?search=Least-squares_spectral_analysis" title="Least-squares spectral analysis">Least-squares spectral analysis</a></li>
<li><a href="/info/en/?search=Wavelet" title="Wavelet">Wavelet</a></li>
<li><a href="/info/en/?search=Whittle_likelihood" title="Whittle likelihood">Whittle likelihood</a></li></ul>
</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/info/en/?search=Survival_analysis" title="Survival analysis">Survival</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/info/en/?search=Survival_function" title="Survival function">Survival function</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Kaplan%E2%80%93Meier_estimator" title="Kaplan–Meier estimator">Kaplan–Meier estimator (product limit)</a></li>
<li><a href="/info/en/?search=Proportional_hazards_model" title="Proportional hazards model">Proportional hazards models</a></li>
<li><a href="/info/en/?search=Accelerated_failure_time_model" title="Accelerated failure time model">Accelerated failure time (AFT) model</a></li>
<li><a href="/info/en/?search=First-hitting-time_model" title="First-hitting-time model">First hitting time</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/info/en/?search=Failure_rate" title="Failure rate">Hazard function</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Nelson%E2%80%93Aalen_estimator" title="Nelson–Aalen estimator">Nelson–Aalen estimator</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">Test</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Log-rank_test" class="mw-redirect" title="Log-rank test">Log-rank test</a></li></ul>
</div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Applications" style="font-size:114%;margin:0 4em"><a href="/info/en/?search=List_of_fields_of_application_of_statistics" title="List of fields of application of statistics">Applications</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/info/en/?search=Biostatistics" title="Biostatistics">Biostatistics</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Bioinformatics" title="Bioinformatics">Bioinformatics</a></li>
<li><a href="/info/en/?search=Clinical_trial" title="Clinical trial">Clinical trials</a> / <a href="/info/en/?search=Clinical_study_design" title="Clinical study design">studies</a></li>
<li><a href="/info/en/?search=Epidemiology" title="Epidemiology">Epidemiology</a></li>
<li><a href="/info/en/?search=Medical_statistics" title="Medical statistics">Medical statistics</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/info/en/?search=Engineering_statistics" title="Engineering statistics">Engineering statistics</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Chemometrics" title="Chemometrics">Chemometrics</a></li>
<li><a href="/info/en/?search=Methods_engineering" title="Methods engineering">Methods engineering</a></li>
<li><a href="/info/en/?search=Probabilistic_design" title="Probabilistic design">Probabilistic design</a></li>
<li><a href="/info/en/?search=Statistical_process_control" title="Statistical process control">Process</a> / <a href="/info/en/?search=Quality_control" title="Quality control">quality control</a></li>
<li><a href="/info/en/?search=Reliability_engineering" title="Reliability engineering">Reliability</a></li>
<li><a href="/info/en/?search=System_identification" title="System identification">System identification</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/info/en/?search=Social_statistics" title="Social statistics">Social statistics</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Actuarial_science" title="Actuarial science">Actuarial science</a></li>
<li><a href="/info/en/?search=Census" title="Census">Census</a></li>
<li><a href="/info/en/?search=Crime_statistics" title="Crime statistics">Crime statistics</a></li>
<li><a href="/info/en/?search=Demographic_statistics" title="Demographic statistics">Demography</a></li>
<li><a href="/info/en/?search=Econometrics" title="Econometrics">Econometrics</a></li>
<li><a href="/info/en/?search=Jurimetrics" title="Jurimetrics">Jurimetrics</a></li>
<li><a href="/info/en/?search=National_accounts" title="National accounts">National accounts</a></li>
<li><a href="/info/en/?search=Official_statistics" title="Official statistics">Official statistics</a></li>
<li><a href="/info/en/?search=Population_statistics" class="mw-redirect" title="Population statistics">Population statistics</a></li>
<li><a href="/info/en/?search=Psychometrics" title="Psychometrics">Psychometrics</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/info/en/?search=Spatial_analysis" title="Spatial analysis">Spatial statistics</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/info/en/?search=Cartography" title="Cartography">Cartography</a></li>
<li><a href="/info/en/?search=Environmental_statistics" title="Environmental statistics">Environmental statistics</a></li>
<li><a href="/info/en/?search=Geographic_information_system" title="Geographic information system">Geographic information system</a></li>
<li><a href="/info/en/?search=Geostatistics" title="Geostatistics">Geostatistics</a></li>
<li><a href="/info/en/?search=Kriging" title="Kriging">Kriging</a></li></ul>
</div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div>
<ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="https://upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="https://upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span><b><a href="/info/en/?search=Category:Statistics" title="Category:Statistics">Category</a></b></li>
<li><b><span class="noviewer" typeof="mw:File"><a href="/info/en/?search=File:Nuvola_apps_edu_mathematics_blue-p.svg" class="mw-file-description"><img alt="icon" src="https://upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/28px-Nuvola_apps_edu_mathematics_blue-p.svg.png" decoding="async" width="28" height="28" class="mw-file-element" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/42px-Nuvola_apps_edu_mathematics_blue-p.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/56px-Nuvola_apps_edu_mathematics_blue-p.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span> <a href="/info/en/?search=Portal:Mathematics" title="Portal:Mathematics">Mathematics portal</a></b></li>
<li><span class="noviewer" typeof="mw:File"><span title="Commons page"><img alt="" src="https://upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="https://upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span><b><a href="https://commons.wikimedia.org/wiki/Category:Statistics" class="extiw" title="commons:Category:Statistics">Commons</a></b></li>
<li><span class="noviewer" typeof="mw:File"><span title="WikiProject"><img alt="" src="https://upload.wikimedia.org/wikipedia/commons/thumb/3/37/People_icon.svg/16px-People_icon.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/3/37/People_icon.svg/24px-People_icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/37/People_icon.svg/32px-People_icon.svg.png 2x" data-file-width="100" data-file-height="100" /></span></span> <b><a href="/info/en/?search=Wikipedia:WikiProject_Statistics" title="Wikipedia:WikiProject Statistics">WikiProject</a></b></li></ul>
</div></td></tr></tbody></table></div></div>' |
Whether or not the change was made through a Tor exit node (tor_exit_node) | false |
Unix timestamp of change (timestamp) | '1713588037' |