Question

What is a pooled variance?

Answer 1

`((n_1-1)s_1^2+(n_2-1)s_2^2)/(n_1+n_2-2)`

Explanation:

Let consider we have two sets of data with `n_1` and `n_2` size. Also consider their variances as `s_1^2` and `s_2^2`. Then pooled variance means the variance of combined data sets with size `n_1+n_2` and it is defined as

`((n_1-1)s_1^2+(n_2-1)s_2^2)/(n_1+n_2-2)`

You can combine more than two data sets also. If you have data sets with sizes `n_1, n_2 .... n_k` and variances `s_1^2, s_2^2 .... s_k^2` then pooled variance is defined as

`((n_1-1)s_1^2+(n_2-1)s_2^2+...+(n_k-1)s_k^2)/(n_1+n_2+...+n_k-k)`

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