Arithmetic Mean

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What is the 'Arithmetic Mean'

The arithmetic mean is a mathematical representation of the typical value of a series of numbers, computed as the sum of all the numbers in the series divided by the count of all numbers in the series. The arithmetic mean is sometimes referred to as the average or simply as the mean. Some mathematicians and scientists prefer to use the term "arithmetic mean" to distinguish it from other measures of averaging, such as the geometric mean and the harmonic mean.

BREAKING DOWN 'Arithmetic Mean'

Nearly every field in mathematics and science uses the arithmetic mean. Many of the most common metrics in economics, such as per capita income and per capita gross domestic product (GDP), are calculated using arithmetic mean.

Suppose you wanted to know what the arithmetic mean of a stock's closing price was over the past week. If the stock closed at $14.50, $14.80, $15.20, $15.50 and then $14, its arithmetic mean closing price would be equal to the sum of the five numbers, $74, divided by 5, or $14.80.

Benefits of Arithmetic Mean

Perhaps the biggest benefit of using the arithmetic mean as a statistical measure is its simplicity. Anyone capable of simple addition followed by division can calculate the arithmetic mean of a data set. Of all the measures of central tendency, the arithmetic mean is least affected by fluctuations when multiple data sets are extracted from a larger population.

Limitations of Arithmetic Mean

In data sets that are skewed or where outliers are present, calculating the arithmetic mean often provides a misleading result. Consider a situation where 10 people are sitting at a restaurant table. Nine of them are teachers earning annual incomes of $45,000, while the 10th is a Silicon Valley entrepreneur who hit it big and earns $5 million per year. The arithmetic mean of their annual incomes is $540,500. This figure, however, in no way represents what the typical person at the table earns.

For data sets that do not follow a normal distribution pattern as represented by the bell curve, it is helpful to compare the arithmetic mean with other statistical measures, such as the median. In the above example, the median income at the table – the income at which half the people studied are above it and half are below it – is $45,000. This figure better represents the group as a whole than the arithmetic mean does. When the median and mean are far apart, as they are in this example, it indicates the data is skewed in the direction of the mean.