How do you figure this out?

Question

For a population that has a standard deviation of 10, what is the standard deviation of the distribution of means for samples of size 2?

A-6.33
B-7.07
C-2
D-3.03

Answer 1

The variance of the population is 100.

variance sample= populationvariance/n*

= 100/2=50
sample standard deviation: sqrt 50 or 7.07

This is widely used, however it is very "flaky" data. A better estimate is to put n-1 in the denominator, but anyone sampling with a sample of size two, is not anticipating very useful information anyway.