# How to Calculate the Mean, Median, & Mode

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The mean, median and mode are measures of central tendency and may also be referred to collectively as types of averages. The term “mean” in the context of statistics refers specifically to the arithmetic mean since there are other types of means, such as the geometric mean or harmonic mean. The arithmetic mean is also frequently referred to as “the average” in common usage, although this is mathematically imprecise, since there are other types of averages.

Define some statistical terms. All measures of central tendency are calculated from a collection of numbers known as a data set. Each member of a data set is also known as a data point.

Determine the arithmetic mean of a data set. The arithmetic mean is defined as the sum of the data points divided by the number of data points. Thus, a data set consisting of 12, 15, 16 and 19 would have an arithmetic mean of (12 + 15 + 16 + 19)/4 = 62/4 = 15.5

Evaluate the median of a data set with an odd number of data points. Arrange the data points in ascending order of value. The median will be the “middle” data point such that half the remaining data points are less than or equal to the median and the other half of the remaining data points are greater than or equal to the median. For example, the median of the data set {1, 2, 2, 3, 4} is 2.

Find the median of a data set with an even number of data points. Arrange the data points in ascending order of value. The median will be the sum of the two “middle” data points divided by 2. For example, the median of the data set {1, 2, 2, 3, 4, 5} is (2 + 3)/2 = 2.5.

Calculate the mode of a data set. The mode is defined as the value in the data set that occurs most often. If more than one value occurs an equal number of times, all of these values are modes for the data set. For example, 2 and 3 are both modes for the data set (1, 2, 2, 3, 3, 4).

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