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Five-number summaries

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A five-number summary is especially useful in descriptive analyses or during the preliminary investigation of a large data set. A summary consists of five values: the most extreme values in the data set (the maximum and minimum values), the lower and upper quartiles, and the median. These values are presented together and ordered from lowest to highest: minimum value, lower quartile (Q1), median value (Q2), upper quartile (Q3), maximum value.

These values have been selected to give a summary of a data set because each value describes a specific part of a data set: the median identifies the centre of a data set; the upper and lower quartiles span the middle half of a data set; and the highest and lowest observations provide additional information about the actual dispersion of the data. This makes the five-number summary a useful measure of spread.

A five-number summary can be represented in a diagram known as a box and whisker plot. In cases where we have more than one data set to analyse, a five-number summary with a corresponding box and whisker plot is constructed for each.

To illustrate the five-number summary of Example 2 in the Range and quartiles section would be 1, 17, 26, 42, 57.