4.8.2 Median
The median is the middle value of a set of numbers arranged in ascending (or descending) order. If the set has an even number of values then the median is the mean of the two middle numbers. For example:
| 1, 1, 2, 5, 8, 10, 12, 15, 24 | This set of nine values is arranged in ascending order and the median is 8. |
| 32, 25, 20, 16, 14, 11, 9, 9, 4, 0 | This set of 10 values is arranged in descending order and here the median is (14 + 11) + 2, which is 12.5. |
The salaries considered in the discussion above are in ascending order and the median is 28 000 euros. This value is more representative of the state of affairs in the company than the mean (41 286 euros) as half the employees earn less than the median and half earn more.
Activity 13
Consider the scores of one batsman during the cricket season:
0, 0, 0, 4, 7, 10, 12, 15, 24, 30, 42, 48
Calculate the median and the mean of this set of scores.
Discussion
| The median = (10 + 12) + 2 = 11 | The mean = 192 ÷ 12 = 16 |
The median is not appropriate here as the number of runs may vary greatly during the season and will probably include a number of zeros. The average actually used to rank players is the mean.