Statistics

Median of a Distribution

In a distribution of the ordered values of a quantitative statistical attribute, the median is a value for which the number of values that are less than it is equal to the number of values that are greater than it.
  • The median of a distribution is not always a datum in the distribution, especially when there is an even number of data in the distribution.
  • The median only depends on the number of data in the distribution and not their individual values.
  • Most often, the median of a distribution is different from its arithmetic mean

Notation

The median of a distribution is noted as “Med” and is read as “median.”

Example

Consider the distribution of these data: 2, 2, 5, 8, 10, 10, 15, 16, 22.
  • The median of this distribution, or the central value, is 10, so we write: Med = 10.
If we consider the distribution: 10, 15, 15, 17, 22, 45, a distribution that includes an even number of data, then generally, the median is the arithmetic mean of the two central values, which are 15 and 17 here. In this case, the median is not necessarily a value in the distribution.
  • Therefore, the median is 16 and we write: Med = 16.

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