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What is the Median?

The median is the middle value of a sorted data set. It divides the data in half: 50% of values fall below it, 50% above. Unlike the mean, it is not pulled by extreme values.

How to Find the Median

  1. Sort all values from smallest to largest
  2. If n is odd: the median is the value at position (n + 1) / 2
  3. If n is even: the median is the average of the values at positions n/2 and n/2 + 1

Worked Examples

Odd count — Data: 3, 7, 8, 12, 20 (n = 5, already sorted)
Middle position: (5 + 1) / 2 = 3rd value → median = 8

Even count — Data: 3, 7, 8, 12 (n = 4)
Two middle values (2nd and 3rd): 7 and 8 → median = (7 + 8) / 2 = 7.5

Why the Median Resists Outliers

Compare two similar data sets:

Set A: 10, 12, 14, 16, 200 → Mean = 50.4, Median = 14
Set B: 10, 12, 14, 16, 18 → Mean = 14, Median = 14

Replacing 18 with 200 leaves the median unchanged but raises the mean from 14 to 50.4. The median sees only the position of values in the sorted list — extreme values cannot pull it away from the centre.

When to Use the Median

Prefer the median when:

  • Your data contains outliers (very high or low values)
  • The distribution is skewed — e.g., household income, house prices, response times
  • You want the value that splits the group 50 / 50

National income statistics, real-estate reports, and medical response times almost always use the median for this reason. Use the statistics calculator to compare both on your own data.

Frequently asked questions

Not necessarily. For an even-count data set the median is the average of the two middle values, which may not appear in the original list. For example, the median of [3, 7] is (3+7)/2 = 5.
When n is even, there are always two middle values. Take their average. For example, [1, 3, 5, 7] → median = (3 + 5) / 2 = 4.
When the distribution is left-skewed (a long tail on the left). A cluster of very low values pulls the mean below the median. This is less common than right-skewed distributions.
No. For symmetric distributions without outliers, the mean and median are similar and both valid. The mean is preferred when you need to compute further statistics such as standard deviation or confidence intervals.
They are the same. The median is the 50th percentile, which is also the second quartile (Q2). It splits the sorted data into the lower and upper halves.
Related guides
What is the mean? What is the median? What is the mode? Standard deviation explained Mean vs median

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