Mean, Median and Mode Calculator

How it works

Mean, median and mode are three different answers to "what is a typical value?". The mean adds everything up and shares it out equally. The median is the middle value once the list is sorted, so half the values are below it and half above. The mode is the value that occurs most often.

They agree when the data are symmetric and disagree when they are not. A few very large values pull the mean up but leave the median where it is, which is why house prices and incomes are usually reported as medians. The mode is the only one of the three that works for categories as well as numbers, and the only one that can be more than one value.

Type or paste your numbers separated by commas, spaces or new lines. The sorted list is shown so you can see where the median falls.

Formula

mean   = (x₁ + x₂ + … + xₙ) ÷ n
median = middle value of the sorted list          (n odd)
       = mean of the two middle values            (n even)
mode   = the value(s) that occur most often; none if every value is unique

Example

Twelve test scores: 85, 92, 78, 92, 88, 75, 95, 92, 81, 88, 70, 90. They add up to 1,026, so the mean is 1,026 ÷ 12 = 85.5.

Sorted they read 70, 75, 78, 81, 85, 88, 88, 90, 92, 92, 92, 95. With twelve values the median is the mean of the sixth and seventh, (88 + 88) ÷ 2 = 88. The score 92 appears three times, more than any other, so the mode is 92. The minimum is 70 and the maximum 95.

Assumptions and limitations

• The mode is reported only when some value appears at least twice. When several values tie for the highest count, all of them are listed.
• Values are compared exactly: 2.5 and 2.50 are the same value, 2.5 and 2.51 are not. Round your data first if you want a mode by class.
• Every entry must be a number. Text such as units or labels in the list stops the calculation and names the offending entry.

Frequently asked questions