What is a pooled variance?

1 Answer
Oct 27, 2015

((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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