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

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

Thanks

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- Jun 26th 2009, 11:12 AMjschlarbSample variance equation question
$\displaystyle S^2 = Sum(Xi-X)^2/n-1$

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

Thanks - Jun 26th 2009, 01:15 PMmatheagle
the data is $\displaystyle X_1, X_2,\ldots X_n$

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

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

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

OR

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