Measures of central tendency

To understand a set of numbers, we often want one value that represents it: a measure of central tendency. There are three.

• Mean (the average) = sum of all values ÷ number of values. It uses every value, but a single outlier (an exceptionally large or small value) can pull it a long way.
• Median = the middle value when the data is sorted. With an even number of values, it is the average of the two middle ones. Outliers barely affect it.
• Mode = the value that occurs most often. A data set may have no mode, or several. Unlike mean and median, the mode also works for non-numeric data, such as the most popular car colour.

Example: the heights (in cm) of nine children are 90, 102, 110, 115, 85, 90, 100, 110, 110.

• Mean = 912 ÷ 9 = 101.33 cm.
• Median: sorted, they are 85, 90, 90, 100, 102, 110, 110, 110, 115; the middle (5th) value is 102 cm.
• Mode: 110 occurs three times, more than any other: 110 cm.