What Is the Arithmetic Mean?

The arithmetic mean is one of the most commonly used measures for summarizing a set of numerical values. It is defined as follows:

$$\overline{x} = \frac{x_1+x_2+\cdots+x_n}{n} = \frac{\sum_{i=1}^{n}x_i}{n}$$

• $x_i$: an individual measurement
• $n$: the number of measurements

For example, if the measured values are $4$, $5$, $6$, $7$, and $8$, the arithmetic mean is:

$$\overline{x} = \frac{4+5+6+7+8}{5} = 6$$

In the graph below, each point represents an individual measurement, while the dashed line represents the arithmetic mean.

Mean = 6

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4

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8

Measurement number

Measured value

The arithmetic mean works well when the data are roughly symmetric and contain no significant outliers. Because extreme values can strongly affect the mean, the median may be more appropriate when the data are skewed or contain outliers.