Formula
\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}Used to calculate: The average value of a set of numerical values.
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What Is the Arithmetic Mean Formula?
The arithmetic mean formula calculates the average of a set of numerical values. It is found by adding all values in the data set and dividing their sum by the number of values.
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Formula and Variables
\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}| Symbol | Meaning | Unit |
| Arithmetic mean of the values | Same unit as the values | |
Individual value in the data set | Depends on the data | |
| Number of values in the data set | None | |
Summation of the specified values | Same unit as the values |
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How to Use the Formula
Add all of the numerical values in the data set, then determine how many values are present. Divide the sum by the number of values to obtain the arithmetic mean.
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When Is This Formula Used?
The arithmetic mean formula is used to find a representative average for a collection of numerical values.
Common uses:
– Calculating averages in data sets
– Summarizing measurements or observations
– Analyzing numerical data in mathematics, statistics, science, and finance
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Important Notes
– The arithmetic mean uses every value in the data set and is sensitive to unusually large or small values.
– The number of values n must be greater than zero; the arithmetic mean of an empty data set is undefined.
– The values being averaged should represent compatible quantities, and the arithmetic mean has the same unit as those values.
– A common point of confusion is treating the arithmetic mean as interchangeable with the median or mode; these are different measures of central tendency.
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Alternate Forms
Alternate form:
\bar{x} = \frac{x_1 + x_2 + \cdots + x_n}{n}Alternate form:
\sum_{i=1}^{n} x_i = n\bar{x}—
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