Level 4 · Ages 13–15
Read it again any time, including while you work through the exercises.
You already know the mean. Here are two new tools to describe a series of numbers: the median and the range.
The median is the middle value when the series is sorted in increasing order: as many values before it as after it. Picture 5 runners lined up from slowest to fastest: the median runner is the 3rd, right in the centre. For the series 3, 7, 8, 12, 15, the median is 8.
Golden rule: ALWAYS sort the series before looking for the middle. That is mistake number one! And if the series has an even number of values, there is no value exactly in the middle: the median is then the mean of the two central values. For 5, 9, 11, 15, the median is (9 + 11) ÷ 2 = 10.
The range measures spread: range = biggest value minus smallest value. For 3, 7, 8, 12, 15: the range is 15 - 3 = 12. A big range means very spread-out values, a small range means tightly grouped values.
Why is the median useful when we already have the mean? Because it resists extreme values. In the series 1, 1, 2, 3, 93, the mean is 20 (because of the 93), but the median is 2, which describes the series much better. Mean and median each tell their own version of the story: a good statistician looks at both.
Here are 5 scores: 3, 7, 8, 12, 15. Find the median and the range.
3, 7, 8, 12, 15 (déjà rangé)
First I check that the series is sorted in increasing order. It is.
milieu : 3e valeur -> 8
There are 5 values: the middle one is the 3rd, with 2 values before and 2 after. The median is 8.
15 - 3 = 12
The range is the biggest value minus the smallest: 15 minus 3 equals 12.
Result: Median: 8. Range: 12.
Here are 4 temperatures: 5, 9, 11, 15. Find the median.
4 valeurs -> 2 valeurs centrales : 9 et 11
With an even number of values, there is no single middle value: I spot the two central values, 9 and 11.
(9 + 11) ÷ 2 = 10
The median is the mean of these two central values: 20 divided by 2 equals 10.
Result: The median is 10.