Average Calculator

Mean, median, mode and standard deviation explained

"Average" usually means the arithmetic mean, but it is one of several ways to describe the centre of a set of numbers. Choosing the right one avoids misleading conclusions, and this calculator reports all of them together with the spread of your data.

The measures

• Mean: add all values and divide by how many there are. For 12, 15, 18, 20 and 35 the sum is 100, so the mean is 20.
• Median: the middle value after sorting. Here it is 18. With an even count, take the mean of the two middle numbers.
• Mode: the value that appears most often. A set can have no mode, one mode or several.
• Standard deviation: how far values typically sit from the mean. A small figure means the numbers are close together.

When mean and median disagree

One very large or very small value pulls the mean towards it. Monthly incomes of 25,000, 28,000, 30,000, 32,000 and 3,00,000 give a mean of 83,000 but a median of 30,000, which better represents a typical earner. When data is skewed, report the median as well as the mean.

Population versus sample

If your numbers are the whole group, such as every student in one class, use the population standard deviation. If they are a sample taken from a larger group, the sample formula divides by n − 1 instead of n to correct for bias. Check which one the calculator labels before copying the result into a report.

Everyday uses

Students use averages for marks and attendance, shopkeepers for daily sales, and analysts for prices and temperatures. A weighted average is needed when items count unequally, for example subjects with different credits: multiply each value by its weight, add the products and divide by the sum of the weights.

Tips

Enter numbers separated by commas, spaces or new lines, remove stray text, and check for typing errors such as an extra zero, since a single mistake changes the mean noticeably. All calculations happen in your browser.