Average (Mean) Calculator

This average calculator computes the average or mean of a data set. To use the calculator, please provide two or more numbers separated by a comma or semicolon, and then click the "Calculate" button.

What is an average or mean?

An average is a single number that is used to represent some list of numbers. The terms average and mean are often used interchangeably, though an average is more specifically referred to as an arithmetic mean. An average is a measure of central tendency that is commonly used in statistics along with other measures of central tendency such as the mode and median. In statistics, the term "mean" is more commonly used than "average."

It is worth noting that there are different types of mean, such as the geometric mean. When the type of mean is not specified, it is usually safe to assume that the mean being discussed is the arithmetic mean. However, it is good practice to simply specify which mean is being used, so as to avoid any potential confusion.

Averages are used frequently in everyday life. For example, if a parent wants to know whether their child is tall or short for their age, they could find data on the average height of children of the same age and compare the height of their child to this average. Similarly, a student can compare the grade they achieved on an exam to the average grade achieved by the class to determine how well they performed on the exam relative to other students. Since averages are used so widely in everyday life, it is useful to be able to calculate an average.

How to calculate the average?

Calculating an average is relatively straightforward. The average of a list of numbers is the sum of all the numbers, divided by the total number of values. This is represented in mathematical notation using the following formula,

where x_i represents the i^th value, and N is the total number of values. Although this formula may seem complicated for those unfamiliar with summation notation, all the ∑x_i means is that we are finding the sum of all the values of interest. For example, referencing the table below of the weight of 10 children in a preschool, we can determine their average weight as follows:

The x_i is a reference to each of the 10 values. For example, x₁ is the first value in the table, or 30. x₈ is the 8^th value, or 38, and so on. Since there are 10 values, N = 10. Plugging all of these into the average formula yields:

Thus, the average weight of the 10 students in the preschool is 27.4 pounds.