Average calculator, with the steps.

An average calculator finds one number that stands for a whole list. The most common kind is the mean: add the numbers and divide by how many there are. This page works out the mean, median and mode together, plus the range, sum, count, smallest and largest value, the geometric and harmonic mean, the quartiles and any outliers, and it writes out each step. It also has a weighted average mode for grades and prices, and a grouped data mode for numbers that come as ranges.

How to use the average calculator

1. Leave What to work out on Average of a list of numbers.
2. Paste or type your numbers in Numbers. Spaces, commas, tabs and new lines all work, so you can paste a spreadsheet column straight in.
3. Read the big Mean (average) card, then the cards below it for the median, mode, range and the rest.
4. Open Mean, Median and the other step boxes to see how each answer was found.
5. Use Round answers to if you want a set number of decimals, Copy result to copy the answers as text, or Copy link to share your numbers.

A worked example

Take the list 12, 15, 15, 18, 22, 30, 95. There are 7 numbers. They add up to 207, and 207 divided by 7 is 29.5714, so the mean is about 29.57. Sorted, the list is already in order, and the fourth number is 18, so the median is 18. The number 15 appears twice and no other number does, so the mode is 15. The range is 95 − 12 = 83.

The mean is much higher than the median here because of the 95. That is why you should look at more than one average. If a few big numbers pull the mean up, such as a few very high salaries, the median usually describes the typical value better.

Mean, median and mode: which to use

With an even count, the median is the mean of the two middle numbers. For 2, 4, 6, 8 the middle pair is 4 and 6, so the median is 5. If every number appears once, the list has no mode. If two numbers tie for most often, both are listed.

Weighted average

Use a weighted average when some numbers count for more than others. Pick Weighted average, then type one row per line: the value, a space, and its weight. A course with an exam worth 40%, a project worth 30% and homework worth 30% might have scores of 90, 80 and 70. Multiply each score by its weight and add: 90 × 40 + 80 × 30 + 70 × 30 = 3600 + 2400 + 2100 = 8100. The weights add up to 100, and 8100 divided by 100 is 81. A plain average of the three scores would be 80, so the weights made a difference. The weights do not have to add up to 100. The calculator always divides by their total.

Mean of grouped data

When you only know how many values fall in each range, pick Mean of grouped data and type one class per line: lower limit, upper limit, frequency. Each class is counted at its midpoint. With the classes 0 to 10 (3 values), 10 to 20 (7), 20 to 30 (12) and 30 to 40 (5), the midpoints are 5, 15, 25 and 35. Then 3 × 5 + 7 × 15 + 12 × 25 + 5 × 35 = 15 + 105 + 300 + 175 = 595, and 595 divided by the 27 values is 22.04. Because the real values are lost, this is an estimate.

Outliers, geometric and harmonic mean

The outlier check uses a common rule of thumb. Find the first quartile (Q1) and third quartile (Q3), the medians of the lower and upper halves, and their gap, the IQR. A number below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR is flagged. In the example, Q1 is 15, Q3 is 30 and the IQR is 15, so the fences are −7.5 and 52.5, and 95 is flagged. A flag is a prompt to look at the number, not proof that it is wrong. Other tools split the halves differently and can give slightly different quartiles.

The geometric mean multiplies the numbers and takes the root, and suits growth rates and ratios. The harmonic mean suits rates such as speed. Both need numbers above zero, and the page says so when they cannot be worked out.

Common problems

• A number is missing from the count: it may have a letter or symbol in it. The page lists anything it skipped.
• Thousands separators: a comma splits numbers here, so type 1200, not 1,200.
• A decimal comma, as in 2,5, is read as two numbers. Use a decimal point.

To go from a mean to a spread, try the standard deviation calculator. For percentages of a total, use the percentage calculator, and for sums with fractions, the fraction calculator.