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Mean, median, mode and range calculator

Type or paste a list of numbers. You get all four measures, with the sum, the ordered list and the working for each.

Find the mean, median, mode and range

Try:

Mean 6

  • Median 6
  • Mode 8
  • Range 5
  • 7 values, total 42

The working

  1. Count the values: there are 7 values.
  2. Add them up: 4 + 8 + 6 + 5 + 3 + 8 + 8 = 42.
  3. Mean: divide the total by the count. 42 ÷ 7 = 6.
  4. Put the values in order: 3, 4, 5, 6, 8, 8, 8.
  5. Median: 7 is odd, so the median is the middle value, number 4 in the ordered list: 6.
  6. Mode: 8 appears 3 times, more often than any other value.
  7. Range: largest minus smallest. 8 − 3 = 5.

How it works

Mean

The mean is what most people call the average: add the values and divide by how many there are. It uses every value, so one unusually large or small number can pull it a long way.

Median

The median is the middle value once the list is in order. With an even number of values there are two in the middle, and the median is halfway between them. It is not affected by extreme values, which is why it is used for things like house prices and salaries.

Mode

The mode is the value that appears most often. A list can have one mode, several, or none at all if every value appears the same number of times. It is the only one of the four that also works for things that are not numbers, such as shoe sizes sold or favourite colours.

Range

The range is the largest value minus the smallest. It is a quick measure of how spread out the values are, not an average. Two lists can share the same mean and have very different ranges.

Typing a list

Separate values with commas, spaces or new lines, and use a point for decimals. Because commas separate values here, write one thousand as 1000 and not 1,000.

Worked examples

Find the mean, median, mode and range of 3, 7, 7, 2, 9, 4

Mean ≈ 5.333333

  • Median 5.5
  • Mode 7
  • Range 7
  • 6 values, total 32
  1. Count the values: there are 6 values.
  2. Add them up: 3 + 7 + 7 + 2 + 9 + 4 = 32.
  3. Mean: divide the total by the count. 32 ÷ 6 ≈ 5.333333.
  4. Put the values in order: 2, 3, 4, 7, 7, 9.
  5. Median: 6 is even, so the median is halfway between the two middle values, 4 and 7: (4 + 7) ÷ 2 = 5.5.
  6. Mode: 7 appears 2 times, more often than any other value.
  7. Range: largest minus smallest. 9 − 2 = 7.

A list with an odd count: 12, 15, 11, 18, 14

Mean 14

  • Median 14
  • Mode none
  • Range 7
  • 5 values, total 70
  1. Count the values: there are 5 values.
  2. Add them up: 12 + 15 + 11 + 18 + 14 = 70.
  3. Mean: divide the total by the count. 70 ÷ 5 = 14.
  4. Put the values in order: 11, 12, 14, 15, 18.
  5. Median: 5 is odd, so the median is the middle value, number 3 in the ordered list: 14.
  6. Mode: every value appears once, so there is no mode.
  7. Range: largest minus smallest. 18 − 11 = 7.

Common questions

What is the difference between the mean and the median?

The mean is the total divided by the count. The median is the middle value in order. For 1, 2, 3, 4, 90 the mean is 20 and the median is 3, so the median describes a typical value better when one number is far from the rest.

Can a set of numbers have no mode?

Yes. If every value appears the same number of times, no value is more common than the others, so there is no mode.

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