By Amy S. Jorgensen
Updated Aug 30, 2022
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Whether you’re a math student, survey designer, statistician, or researcher, you’ll often need to compute the average of a set of numbers. In mathematics and statistics, the average can be derived in three distinct ways: the mean, the median, and the mode.
The mean, or arithmetic average, is perhaps the most familiar method. To calculate it, sum all of the values and divide by the count of values. For instance, with the set 3, 7, 10, and 16, the total is 36. Dividing by four yields a mean of 9.
The median represents the middle value when the data are arranged in ascending order. If the count is even, the median is the average of the two central numbers. For example, from the ordered list 1, 3, 5, 7, the two middle numbers are 3 and 5; their average, 4, is the median.
The mode is the value that appears most frequently. In the set 12, 12, 16, 16, 16, 25, 36, the number 16 occurs three times and is therefore the mode.
Consider the dataset 125, 65, 40, 210, and 65. The mean is calculated as (125 + 65 + 40 + 210 + 65) ÷ 5 = 101. The median, after ordering the data, is 65, and the mode is also 65. This example illustrates how the mean can differ from the median and mode, especially when the data contain outliers.
For a visual explanation, watch the accompanying video below:
