# What is the mathematical formula for the pooled variance of two populations?

Aug 5, 2016

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

#### Explanation:

The pooled standard deviation is given by
${S}_{p} = \sqrt{\frac{\left({n}_{1} - 1\right) {s}_{1}^{2} + \left({n}_{2} - 1\right) {s}_{2}^{2}}{{n}_{1} + {n}_{2} - 2}}$

for variance remove the sqare root operator

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