# Dictionary:Central limit theorem

A statement about the characteristics of the distribution of the means of random samples. If we could draw an infinite number of random samples of a given size where we calculate the mean of each sample, (a) the mean of the means of the samples equals the mean of the population from which the samples were drawn; (b) the variance of the sampling distributions equals the variance of the population divided by the sample size. (c) If the original population is normally distributed (i.e., is bell-shaped), the sampling distribution will also be bell-shaped, and if the original population is not normally distributed, the distribution will increasingly approximate a normal distribution as the sample size increases.