Arithmetic Mean Formula

This figure illustrates the arithmetic mean formula

Formula

Summary

This formula calculates the arithmetic mean of a dataset. The arithmetic means represents the average value or “balancing point” of a data set.

Expression Description
The arithmetic mean.
The number of data points
the value of the element at the i-th position.

Usage

The arithmetic mean is the average value of a sample space. To calculate the arithmetic mean sum all the data points in a sample space and then divide by the number of elements.

Examples

Example 1

This example shows how to calculate the mean of a data set shown below.

Steps

  1. Start by setting up the formula.

  2. Substitute the data values into the numerator and the size of the dataset into the denominator. In this case, there are six elements in the dataset so .

  3. Calculate the sum of the values.

  4. Calculate the result of the division.

    The mean of the dataset is .

Example 2

This example shows how to calculate the mean of a data set shown below.

Steps

  1. Start by setting up the formula.

  2. Substitute the data values into the numerator and the size of the dataset into the denominator. In this case, there are five elements in the dataset so .

  3. Calculate the sum of the values.

  4. Calculate the result of the division.

    The mean of the dataset is .