The variance of a sample is a random variable which can be used as an

estimator of the population variance (and will be unbiased if the correct

variant is used). As such it is approximatly equal to the population

variance, and the approximation is (probably) better for a larger sample

than for a smaller sample.

The variance of the mean of a sample is what gets smaller as the sample

size goes up, and this variance is inversly proportional to the square

root of the sample size.

RonL