Average Calculator

The calculator reads a plain list, so you can paste a column from a spreadsheet, a line from a report or a handful of numbers you typed yourself.

1. Enter your values in the Numbers (separated by commas, spaces or new lines) box. The box starts with 12, 15, 15, 18, 22, 30 so you can see the layout. Semicolons also work as separators.
2. Set Decimal places from 0 to 10. The default of 2 suits most lists, while a higher setting helps with small standard deviations.
3. Read the mean at the top, then the table: count, sum, mean, median, mode, smallest, largest, range, first and third quartile, both kinds of standard deviation and variance, and the geometric mean.
4. Check the note under the mean. Any entry that is not a number, such as a word, a currency sign or a percent sign, is skipped and counted so you know it was left out.
5. Edit the list or the decimal places to see the figures change.

The reference list below is short enough to check by hand, which is a good way to learn what each row means.

Take the list 12, 15, 15, 18, 22, 30. There are 6 values with a sum of 112, so the mean is 18.67. The sorted middle pair is 15 and 18, so the median is 16.5. The value 15 appears twice, which makes it the mode. The range is 30 - 12 = 18. The lower half is 12, 15, 15 and the upper half is 18, 22, 30, so Q1 is 15 and Q3 is 22. The population standard deviation is 5.93, the sample standard deviation is 6.50 and the geometric mean is 17.83.

For 2 4 4 4 5 5 7 9 the mean is 5, the median is 4.5 and the mode is 4. The squared distances from the mean add up to 32, so the population variance is 32 / 8 = 4 and the population standard deviation is exactly 2. The sample version divides by 7 instead, giving a variance of 4.5714 and a standard deviation of 2.1381 at four decimal places.

Now add one extreme value, 300, to the first list. The mean jumps to 58.86 while the median only moves to 18. That gap is the usual sign that one outlier is pulling the mean.

Use the mean when values are fairly even and you want every one to count. Use the median for skewed data such as wages or property prices, where a few large values distort the mean. The mode suits repeated values, though it is less useful for measurements that rarely repeat. Choose the geometric mean for growth rates and ratios. For standard deviation, use the sample version when your numbers are a sample of a bigger group, and the population version when they are the whole group.

• A decimal comma is read as a separator, so 3,5 becomes the two numbers 3 and 5. Write 3.5 instead.
• There is no weighted average, so repeat a value to give it more weight.
• Quartile methods differ between textbooks and spreadsheets, so Q1 and Q3 may differ slightly from other software.

To put a list in order first, use the number sorter. To express a mean as a share of a total, try the percentage calculator or the fraction calculator.