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To clear something up; I use "Eulerian n+1-tuple" for all n>2 when we need n nth powers summing to an nth power; this is a generalization of a Pythagorean triple that must be distinguished from a "Pythagorean n+1-tuple", which means n squares sum to a square.
Because SSSS doesn't prove a unique shape and size of a quadrilateral, no theorem exists relating Eulerian quadruples to the sides of a quadrilateral where each side has that number of units long (that is, we can't know the exact shape and size of a quadrilateral whose sides are 3, 4, 5, and 6 units long.) But what about proving a tetrahedron's shape and size from the areas of its faces?? That is, if we had a tetrahedron whose face areas have 3, 4, 5, and 6 square units; what does this show about the tetrahedron?? (In case you're wondering, 3,4,5,6 is an Eulerian quadruple because 3^3+4^3+5^3=6^3.) Georgia guy ( talk) 15:46, 24 September 2022 (UTC)
What is the largest set of datapoints that cannot contain any outliers? I want to say 2 but I don’t know if that’s right. Duomillia ( talk) 19:01, 24 September 2022 (UTC)
There is no absolute agreement among statisticians about how to define outliers". [1] A common definition is: a data point that is very different from the rest of the data. [2] [3] [4] To apply this definition, a measure of this difference is needed, as well as a threshold separating "very" from "not very". If the data appears to follow a normal distribution, one can use its distance to the central tendency, divided by the square root of the variance. Somewhat arbitrarily, one can then set a threshold of, say, five sigma. If someone sees a normal distribution when looking at a five-point data set, my diagnosis is that they are suffering from statistical pareidolia. One needs a model for the distribution of "normal" points based either on a priori considerations, or because it is strongly suggested by the data. -- Lambiam 21:24, 24 September 2022 (UTC)
Mathematics desk | ||
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< September 23 | << Aug | September | Oct >> | Current desk > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
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The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
To clear something up; I use "Eulerian n+1-tuple" for all n>2 when we need n nth powers summing to an nth power; this is a generalization of a Pythagorean triple that must be distinguished from a "Pythagorean n+1-tuple", which means n squares sum to a square.
Because SSSS doesn't prove a unique shape and size of a quadrilateral, no theorem exists relating Eulerian quadruples to the sides of a quadrilateral where each side has that number of units long (that is, we can't know the exact shape and size of a quadrilateral whose sides are 3, 4, 5, and 6 units long.) But what about proving a tetrahedron's shape and size from the areas of its faces?? That is, if we had a tetrahedron whose face areas have 3, 4, 5, and 6 square units; what does this show about the tetrahedron?? (In case you're wondering, 3,4,5,6 is an Eulerian quadruple because 3^3+4^3+5^3=6^3.) Georgia guy ( talk) 15:46, 24 September 2022 (UTC)
What is the largest set of datapoints that cannot contain any outliers? I want to say 2 but I don’t know if that’s right. Duomillia ( talk) 19:01, 24 September 2022 (UTC)
There is no absolute agreement among statisticians about how to define outliers". [1] A common definition is: a data point that is very different from the rest of the data. [2] [3] [4] To apply this definition, a measure of this difference is needed, as well as a threshold separating "very" from "not very". If the data appears to follow a normal distribution, one can use its distance to the central tendency, divided by the square root of the variance. Somewhat arbitrarily, one can then set a threshold of, say, five sigma. If someone sees a normal distribution when looking at a five-point data set, my diagnosis is that they are suffering from statistical pareidolia. One needs a model for the distribution of "normal" points based either on a priori considerations, or because it is strongly suggested by the data. -- Lambiam 21:24, 24 September 2022 (UTC)