What is a pooled variance?

1 Answer
Oct 27, 2015

Answer:

#((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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