How To Calculate Variance From Standard Error

In statistics, the standard error of a sampling statistic indicates the variability of that statistic from sample to sample. Thus, the standard error of the mean indicates how much, on average, the mean of a sample deviates from the true mean of the population. The variance of a population indicates the spread in the distribution of a population. For instance, the variance in the ages of all the children in a daycare center will be much less than the variance in ages of all the people (children and adults) who live in an entire county. While the variance and the standard error of the mean are different estimates of variability, one can be derived from the other.

Step 1

Multiply the standard error of the mean by itself to square it. This step assumes that the standard error is a known quantity.

Step 2

Count the number of observations that were used to generate the standard error of the mean. This number is the sample size.

Step 3

Multiply the square of the standard error (calculated previously) by the sample size (calculated previously). The result is the variance of the sample.