Calculating Sample Variance for the Combined Data

There are times when we need more sample to achieve a more accurate estimator. Since these two sets of sample have the information about the same population, it is necessary to treat both as a single combined data. In this paper we present the unpooled sample variance for the combined data when we just know a sample mean and variance for the each data set without the raw data. It is shown that the pooled variance s(p)(2) is always greater than the exact variance s(t)(2) when (x) over bar (n) = (y) over bar (m). And the difference of means for two data, (x) over bar (n) = (y) over bar (m), is larger, the difference of s(p)(2) and s(t)(2) is larger.