Median Calculator

The median splits your data in half: half the values are at or below it, half at or above. Enter a list to find it.

Median of a list

Separate numbers with commas, spaces or new lines.

Median7.5
Sorted values
3, 4, 7, 8, 9, 12
Count
6
Lower and upper quartile (Q1, Q3)
4, 9

Working

  1. Sort the values from smallest to largest.
  2. There are 6 values (even), so the median is the average of values 3 and 4: (7 + 8) ÷ 2 = 7.5

How the median is found

  • Sort the values from smallest to largest.
  • Odd count: the median is the single middle value, at position (n + 1) ÷ 2.
  • Even count: the median is the mean of the two middle values, at positions n ÷ 2 and n ÷ 2 + 1.

Worked example

Median of 7, 3, 9, 4, 12, 8

  1. Sort: 3, 4, 7, 8, 9, 12
  2. There are 6 values (even), so take values 3 and 4: 7 and 8
  3. Average them: (7 + 8) ÷ 2 = 7.5

The median is 7.5.

Why use the median

The median is resistant to extreme values. Replacing 12 with 1,200 in the example above leaves the median at 7.5, while the mean jumps from 7.17 to 205.17. That is why incomes, house prices and response times are usually summarised with the median.

Quartiles

Quartiles extend the same idea: Q1 is the median of the lower half and Q3 of the upper half, so the middle 50% of the data lies between them. Several textbook conventions exist; this calculator uses the common school method — the median of each half, leaving out the overall median when the count is odd — so results can differ slightly from spreadsheet functions such as QUARTILE.INC on small data sets.