A different formula is used to calculate a standard deviatio

A different formula is used to calculate a standard deviation for a large sample to a small sample. Why?

Solution

We are normally interested in knowing the population standard deviation because our population contains all the values we are interested in. Therefore, you would normally calculate the population standard deviation if:

(1) you have the entire population or

(2) you have a sample of a larger population, but you are only interested in this sample and do not wish to generalize your findings to the population.

However, in statistics, we are usually presented with a sample from which we wish to estimate (generalize to) a population, and the standard deviation is no exception to this. Therefore, if all you have is a sample, but you wish to make a statement about the population standard deviation from which the sample is drawn, you need to use the sample standard deviation. Confusion can often arise as to which standard deviation to use due to the name \"sample\" standard deviation incorrectly being interpreted as meaning the standard deviation of the sample itself and not the estimate of the population standard deviation based on the sample.