Sample mean and sum

The mean of a random sample, , has a distribution that is approximately normal if the sample size, n, is large and alway has a mean and standard deviation that depend on the population mean, µ, and standard deviation, σ,

 =  μ
 = 

Occasionally the sum of values in a random sample values is more useful than the mean,

Its distribution is a scaled version of the distribution of the mean — the same shape but different mean and standard deviation.

Mean vs Sum

As the sample size increases,