The Median

Five friends have 9, 2, 11, 6 and 4 stickers. The median is the middle value, but only once the values are in order: 2, 4, 6, 9, 11. Two values sit on each side of the 6, so the median is 6.

Sorting first is the whole method. The middle position of the list as given holds 11, which is the largest value, not a middle one. The median describes the middle of the data, and the data only has a middle once it is lined up from smallest to largest.

With an even count there is no single middle value. Sorted, 3, 10, 5, 8 becomes 3, 5, 8, 10, and the two middle values are 5 and 8. The median is their mean: (5 + 8) / 2 is 6.5. The median does not care how extreme the ends are: change 10 to 100 and it stays 6.5, while the mean jumps. That is why house prices and salaries are usually reported as medians.