Measures of spread

The range and inter-quartile range are easy to understand and to explain to others. However the value that is most often used to summarise the spread of values in a data set is its standard deviation.

The standard deviation is a 'typical' distance of values from the sample mean.

Brief explanation

The formula for the standard deviation involves the term,

The closer the values to the mean (corresponding to a small spread), the smaller this sum and therefore the smaller the standard deviation.

Variance

The square of the standard deviation, s2, is called the sample variance. However since the standard deviation has the same units as the original data (e.g. kilograms or dollars), it is more easily interpreted.