A friend of yours who knows no statistics reads the followin

A friend of yours who knows no statistics reads the following sentence The standard deviation of sample means of small samples is greater than the standard deviation of sample means of large samples. Briefly explain to your friend in non-technical language what this means and give an example of its application in a simple statistical problem.

Solution

well the standard deviation of sample means is calculate by sigma / srqt (n)

if you have n = 5

and n = 10

and the same sigma (standard deviation of population) = 2

we have

2 / srqt (5) = 0.89

2 / srqt(10) = 0.63

as you can see the standard deviation with you have sample larges is lower than when you have a sample small