Average Calculator

About the Average Calculator

Finds the arithmetic mean (average) of any list of numbers, along with the sum and how many values you entered.

How to use this calculator

1. Enter your numbers as a list, separated by commas or spaces.
2. Check that every value you want included is entered once.
3. Use the calculator to find the sum, count, and mean.
4. Compare the result with your own work to make sure it looks reasonable.

The formula explained

The formula \( \bar{x} = \frac{\sum x_i}{n} \) computes the mean by dividing the total of all values by how many values there are. Here, \( \sum x_i \) is the sum and \( n \) is the count.

• \(\bar{x}\) = the mean, or average
• \(\sum x_i\) = the sum of all values in the list
• n = the number of values in the list
• \(x_i\) = one value from the list

Step by step method

1. Add all the numbers to find the sum.
2. Count how many numbers are in the list.
3. Divide the sum by the count.
4. Write the result as the mean.

Worked example

Problem. Find the average of 8, 12, 15, 5, and 10.

1. Add the numbers: 8 + 12 + 15 + 5 + 10 = 50.
2. Count the values: there are 5 numbers.
3. Divide: 50 ÷ 5 = 10.

Tips and common mistakes

• Do not forget to include every number exactly once, because leaving one out changes the mean.
• If the numbers are decimals, keep them in the sum and divide the same way.

Frequently asked questions