The median is the value that has half of the data below it and half above it. NIST defines it as the value of the point which has half the data smaller than that point. Because it depends on rank, not on the size of each value, extreme values do not distort it, which makes it a better description of a typical value than the arithmetic mean when outliers are present.
How to find it
- Sort the values from smallest to largest.
- If the count n is odd, the median is the value at position (n + 1) ÷ 2.
- If n is even, the median is the mean of the two middle values.
Example
Odd count: 3, 4, 5, 6, 8, 8, 9 has seven values, so the median is the 4th, 6.
Even count: 3, 5, 7, 10 has four values; the middle two are 5 and 7, so the median is (5 + 7) ÷ 2 = 6.
With the electricity bills 42, 45, 47, 48, 50, 52 and 310, the median is $48 while the mean is about $84.86, which shows how one extreme value moves the mean but not the median. The mean, median and mode calculator finds it for any list, and the guide to calculating an average walks through more cases.