Mean, Median, Mode Calculator

Find the mean, median, mode and range of a list of numbers, plus the min, max, sum and count.

Mean (average)
10.8
Frequency of each value (median 10 highlighted)
00.511.523 — Count: 134 — Count: 05 — Count: 16 — Count: 067 — Count: 28 — Count: 19 — Count: 0910 — Count: 011 — Count: 012 — Count: 11213 — Count: 114 — Count: 115 — Count: 01516 — Count: 017 — Count: 018 — Count: 11819 — Count: 020 — Count: 021 — Count: 121
Median
10
Mode
7
Range
18
Minimum
3
Maximum
21
Sum
108
Count
10
Show the working
  1. Sorted: 3, 5, 7, 7, 8, 12, 13, 14, 18, 21
  2. Mean = sum ÷ count = 108 ÷ 10 = 10.8
  3. Median: with n = 10, the two middle values (positions 5 and 6) are 8 and 12, so the median is their average 10
  4. Mode: 7 appears 2 times — more than any other value
  5. Range = max − min = 21 − 3 = 18

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Formula

Mean = (x₁ + x₂ + … + xₙ) ÷ nMedian = middle value of the sorted list (average of the two middle values if n is even)Mode = most frequent valueRange = maximum − minimum

How it works

The mean, median and mode are three ways to describe the “centre” of a data set. The mean is the ordinary average: add everything up and divide by how many values there are. The median is the middle value once the data are sorted. The mode is the value that appears most often.

They can tell different stories. In the list 2, 3, 3, 4, 100, the mean is 22.4 but the median is just 3, because the single large value drags the mean upward. That is why median household income is usually reported instead of mean income — a few very high earners would distort the average.

A data set can have one mode, several modes (bimodal or multimodal), or no mode at all if every value occurs the same number of times. The range — largest minus smallest — is the simplest measure of spread; the standard deviation gives a more complete picture.

Frequently asked questions

When should I use the median instead of the mean?

Use the median when the data are skewed or contain outliers, such as house prices, incomes or reaction times. Use the mean for roughly symmetric data, or when you need the total to matter.

How do I find the median of an even number of values?

Sort the values and take the average of the two in the middle. For 4, 7, 9, 12 the median is (7 + 9) ÷ 2 = 8.

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