Use this free average calculator to find the average (mean) of a list of numbers. Paste your numbers, separated by commas, spaces or new lines, and you get the mean, median, mode and range at once, plus the sum, the count, the smallest and the largest number. A picture shows where your numbers sit, and the steps and the formula are shown. Two more tabs find the average of percentages and scores, such as 48.5/50 (both the simple average and the overall average by total points), and the average of times. Lists to try and a table on when to use the mean, the median or the mode are underneath. It is free and instant, and your numbers stay in your browser.
How to find the average (mean)
The average, more exactly called the mean, is the total of the numbers divided by how many there are. Add them all up and divide by the count. In everyday speech, “average” and “mean” mean the same thing.
sum of the numbers ÷ how many numbersMedian:
the middle number of the sorted listMode:
the number that appears most oftenRange:
largest − smallestExample: 2, 4, 4, 4, 5, 5, 7, 9. The numbers add up to 40 and there are 8 of them, so the mean is 40 ÷ 8 = 5.
Example: 5, 8, 12, 15. The sum is 40 and the count is 4, so the average is 40 ÷ 4 = 10. A list such as 100, 90, 83 has a sum of 273, so its average is 273 ÷ 3 = 91.
Median
The median is the middle number once the list is in order. With an odd number of values it is the one in the middle. With an even number it is the mean of the two middle values. In the first list above the middle two numbers are 4 and 5, so the median is 4.5. For 1, 2, 3, 4 the median is 2.5. The median is not pulled up or down by one very large or very small value, so it is often a fairer picture of a typical number, such as a typical salary or house price. In the list 1, 2, 3, 4, 100 the mean is 22 but the median is 3.
Mode
The mode is the number that appears most often. In 2, 4, 4, 4, 5, 5, 7, 9 it is 4, which appears three times. A list can have more than one mode, like 1, 1, 2, 2, 3, which has modes 1 and 2. If every number appears only once, there is no mode.
Range
The range is the largest number minus the smallest. It shows how spread out the numbers are. In 2, 4, 4, 4, 5, 5, 7, 9 the range is 9 − 2 = 7.
Which average should I use?
- Use the mean when the numbers are fairly even, such as test scores.
- Use the median when a few extreme values could mislead, such as incomes.
- Use the mode for the most common choice, such as a popular shoe size.
How to average percentages
To average percentages, add them up and divide by how many there are. 90%, 85% and 78% have an average of 253 ÷ 3 = 84.33%. Scores such as 48.5/50, 43.5/50 and 28.5/30 are 97%, 87% and 95%, so the simple average is 93%. But if you add up all the points instead, you get (48.5 + 43.5 + 28.5) ÷ (50 + 50 + 30) = 120.5 ÷ 130 = 92.69%. The two answers differ because the tests have different totals. Use the overall answer when every point counts the same, and the simple average when every test counts the same.
Average of times
Change each time into seconds, add them up, divide by how many there are, and change the answer back. 1:30, 2:15 and 1:45 are 90, 135 and 105 seconds. They add up to 330 seconds, and 330 ÷ 3 = 110 seconds, which is 1:50. Write times as m:ss (1:30) or h:mm:ss (1:05:30).
Average of averages
Be careful when you average averages. If one group of 10 people has an average of 80 and another group of 30 people has an average of 60, the overall average is not (80 + 60) ÷ 2 = 70. The bigger group counts for more: (80 × 10 + 60 × 30) ÷ 40 = 65. This is called a weighted average.
Type or paste your numbers above, separated by commas, spaces or new lines. Use a dot for decimals, such as 2.5.
