# What is a pooled variance?

Oct 27, 2015

$\frac{\left({n}_{1} - 1\right) {s}_{1}^{2} + \left({n}_{2} - 1\right) {s}_{2}^{2}}{{n}_{1} + {n}_{2} - 2}$

#### 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

$\frac{\left({n}_{1} - 1\right) {s}_{1}^{2} + \left({n}_{2} - 1\right) {s}_{2}^{2}}{{n}_{1} + {n}_{2} - 2}$

You can combine more than two data sets also. If you have data sets with sizes ${n}_{1} , {n}_{2} \ldots . {n}_{k}$ and variances ${s}_{1}^{2} , {s}_{2}^{2} \ldots . {s}_{k}^{2}$ then pooled variance is defined as

$\frac{\left({n}_{1} - 1\right) {s}_{1}^{2} + \left({n}_{2} - 1\right) {s}_{2}^{2} + \ldots + \left({n}_{k} - 1\right) {s}_{k}^{2}}{{n}_{1} + {n}_{2} + \ldots + {n}_{k} - k}$

Also see the link for further information.
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