Distribution of Normal Means with Different Sample Sizes

Samples of a given size were taken from a normal distribution with mean 52 and standard deviation 14. The distribution of sample means for samples of size 16 (in blue) does not change but acts as a reference to show how the other curve (in red) changes as you move the slider to change the sample size. Distributions of sample means from a normal distribution change with the sample size. This Demonstration lets you see how the distribution of the means changes as the sample size increases or decreases.

The population mean of the distribution of sample means is the same as the population mean of the distribution being sampled from. Thus the mean of the distribution of the means never changes. The standard deviation of the sample means, however, is the population standard deviation from the original distribution divided by the square root of the sample size. Thus as the sample size increases, the standard deviation of the means decreases; and as the sample size decreases, the standard deviation of the sample means increases.

Reference:

Michael Sullivan, Fundamentals of Statistics, Upper Saddle River, NJ: Pearson Education, Inc., 2008 pp. 382–383.