Thread: Variance of mean for uniform distribution (discrete)

Help wanted to calculate the variance of mean of uniform distribution, as below:

Suppose X follows a discrete uniform distribution from 1 to N. Suppose 1,000 sampling process are carried out. In each sampling, n samples are taken from X ( with replacement), and an mean is calculated. After 1,000 repeats, 1000 means are obtained. What is the variance of these means?

I got that. The sd of mean is sqrt((N^2 -1)/(12*n)).