# Variance and sample size

• Jan 19th 2008, 02:57 AM
star_Asia
Variance and sample size
Could someone please explain to me the relationship between variance and sample size. i know that when the sample is small the variance larger (hence, we use students t distribution when estimating small samples). but why exactly is this? i saw a question in a past paper, asking whether or not a large sample will have a smaller variance compared to a smaller sample and i was not sure how to answer. please help!
• Jan 19th 2008, 01:19 PM
CaptainBlack
Quote:

Originally Posted by star_Asia
Could someone please explain to me the relationship between variance and sample size. i know that when the sample is small the variance larger (hence, we use students t distribution when estimating small samples). but why exactly is this? i saw a question in a past paper, asking whether or not a large sample will have a smaller variance compared to a smaller sample and i was not sure how to answer. please help!

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