Sample variance equation question

jschlarb · #1 $Old$ June 26th, 2009, 01:12 PM

$S^2 = Sum(Xi-X)^2/n-1$

I'm not sure what exactly Xi means. Is it the sum of a single data point minus the sample mean squared?

Thanks

matheagle · #2 $Old$ June 26th, 2009, 03:15 PM

the data is $X_1, X_2,\ldots X_n$

You're summing i from 1 to n, and it's $\bar X$ , not X.

$S^2={\sum_{i=1}^n (X_i-\bar X)^2\over n-1}$

$={ (X_1-\bar X)^2 + (X_2-\bar X)^2+(X_3-\bar X)^2+\cdots +(X_n-\bar X)^2 \over n-1}$

OR

$={\sum_{i=1}^n X^2_i-n\bar X^2\over n-1}$