Question

The variance of a distribution of means is smaller than the original population variance because:.

Answer 1

The variance (σ2), is defined as the sum of the squared distances of each term in the distribution from the mean (μ), divided by the number of terms in the distribution (N).

Given a sample from a normal (or asymptotic normal) distribution, the sample variance is more often less than the population variance due to the skewed nature of the distribution of the unbiased sample estimate.