Standard Deviation and Variance of the Mean

If the mean of a population is calculated from a random selection of samples, this mean value for the sample will not correlate exactly with the true mean value for the population. If several samples are taken from the population, then the mean values of these samples will vary, and a standard deviation can also be calculated for this variation. It is known as the standard deviation of the mean (or the standard error of the mean) or the variance of the mean, respectively. The standard deviation or variance of the mean can be calculated from the standard deviation or variance of the samples. It is easy to see that the range of the different mean values must decrease in proportion to the increase in the number of individual samples in the random samples.