The median is the midpoint element of the set of distinct elements in a collection of values.

If the set contains an even number of elements, two elements exist on either side of the middle-point. In this situation, the median is the arithmetic mean of these elements.

If there are n-many elements in the data set, then:

  • if n is odd, the median is x_{n/2}
  • if n is even, the median is \frac{1}{2} \cdot (x_{\frac{n-1}{2}} + x_{\frac{n+1}{2}})

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