the set of rational numbers (gcd(a,b)=1) whose denominator are odd is group under addition?(include zero).

Yes (as long as negatives are also included, of course). It is left as an easy exercise for the reader to prove it. -- Meni Rosenfeld ( talk) 07:31, 22 September 2006 (UTC) reply

Original poster, ignore this: we can also look at that as ${\displaystyle \mathbb {Z} }$ localized at the prime ideal (2), right? Tesseran 08:48, 22 September 2006 (UTC) reply

To be honest, this is the first time I've heard about localization of a ring. If I understand that article correctly, then no - rather, it would be Z localized at the set of odd integers. -- Meni Rosenfeld ( talk) 20:22, 22 September 2006 (UTC) reply

You can localize in multiplicative set, for example odd integers (here You are right), but if one sais "to localize in prime ideal" he means to localize in a multiplicative set consisting of all elements not in a given prime ideal. So "to localize at the prime ideal (2)" means exactly "to localize using multiplicative set of odd numbers".

Oh, okay. -- Meni Rosenfeld ( talk) 06:02, 23 September 2006 (UTC) reply

Furthermore, it's even a ring, isn't it? – b_jonas 18:01, 23 September 2006 (UTC) reply

In statistics, what is exactly the difference between mode, mean and average?"

Usually "mean" and "average" mean the same thing. See our articles on Mode, Mean, and Average. You may also be interested in Median. -- Lambiam ^Talk 15:20, 22 September 2006 (UTC) reply

"Arithmetic mean" is the same as "average", but "geometric mean" is something else. StuRat 15:23, 22 September 2006 (UTC) reply

A distinction should be drawn between the precise meaning of these terms and the popular meaning. In the latter case, "average" nearly always refers to the arithmetic mean, but more precisely it refers to a "typical value", or with more jargon, a "measure of central tendency". Thus any mean, or mode, or median, is an average. (Though the mode, in particular, can be anything but central.)

Again, "mean" without qualification usually refers to the AM, but there are any number of different means which can be calculated from a set of figures, the commonenest are maybe the geometric and harmonic varieties.

It's a great pity that a subject concerned with the careful evaluation of data is cursed with such sloppy usage.-- 86.132.238.249 18:01, 22 September 2006 (UTC) reply

how do I calculate the chi-square in very clear and simple steps? Mariesaintmichel 15:12, 22 September 2006 (UTC)thank you Marie Saint Michel reply

What is the nature of your data? Is it a 2 by 2 contingency table? -- Lambiam ^Talk 15:22, 22 September 2006 (UTC) reply

If you can calculate the expected values, then Pearson's chi-square test tells you the calculation (${\displaystyle \chi ^{2}=\sum _{i=1}^{N}{\frac {({O_{i}-E_{i}})^{2}}{E_{i}}}}$) to use.

For a congintency table, here's a hint:

${\displaystyle {\mbox{expected frequency of cell}}={\frac {{\mbox{row total where cell is}}\times {\mbox{column total where cell is}}}{\mbox{sum of all cell values in contingency table}}}}$

x42bn6 Talk 01:39, 23 September 2006 (UTC) reply