The pooled variance is a method for estimating the variance of several different populations when the means of each population maybe be different but where one may assume that the variance of each population is the same. Under the assumption of equal population variances, the pooled sample variance provides a higher precision estimate of variance than the individual sample variances. The square root of the pooled variance is called the pooled standard deviation, similarly to how the square root of the variance is the standard deviation.
Given a set of sample variances