Mean

Mean

Definition: Mean

The mean is the sum of a set of values, divided by the number of values in the set. The notation for the mean of a set of values is a horizontal bar over the variable used to represent the set, for example \(\bar{x}\). The formula for the mean of a data set \(\{{x}_{1}; {x}_{2};...;{x}_{n}\}\) is:

\begin{align*} \overline{x}& = \cfrac{1}{n}\sum _{i=1}^{n}{x}_{i}\hfill \\ & = \cfrac{{x}_{1} + {x}_{2} + \ldots + {x}_{n}}{n} \end{align*}

The mean is sometimes also called the average or the arithmetic mean.

Example

Question

What is the mean of the data set \(\{10; 20; 30; 40; 50\}\)?

Calculate the sum of the data

\[10 + 20 + 30 + 40 + 50 = 150\]

Divide by the number of values in the data set to get the mean

Since there are \(\text{5}\) values in the data set, the mean is:

\[\text{mean} = \cfrac{150}{5} = 30\]

This lesson is part of:

Statistics and Probability

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