Sample Statistics

# The Sample Standard Deviation

## The Problem

The standard deviation is a measure of how variable the data are. The variance is also a measure of how spread out the data are. The main advantage of the standard deviation over the variance is that the units of the standard deviation are the same as those of the original data. That means the standard deviation can be represented on the same graphic used to represent the data.

Because the standard deviation uses the mean in its calculations, it would only make sense to use the standard deviation if the mean should also have been used. Thus, data that are highly skewed should not use the standard deviation to represent variability. To illustrate calculating the standard deviation, assume that you collected the following 9 data values:

58, 63, 58, 97, 57, 79, 77, 5, 97

Calculate the standard deviation of this sample, s.