Median, mode, outliers and range
Answers are for parents and teachers.
1
Find the mode and the median of 3, 6, 4, 6, 8, 6, 5.
The mode is 6. In order: 3, 4, 5, 6, 6, 6, 8, and the median is 6.
2
Seven pupils have 20, 22, 21, 23, 22, 21 and 95 LE in their money boxes. Which is the outlier? Does it change the median much?
The outlier is 95. In order: 20, 21, 21, 22, 22, 23, 95, the median is 22. Without 95 the median of 20, 21, 21, 22, 22, 23 is (21 + 22) ÷ 2 = 21.5. It changes only a little.
3
Find the range of 31, 28, 35, 40, 26 and of 52, 50, 49, 51, 53. Which set is more spread out?
The first range is 40 − 26 = 14. The second is 53 − 49 = 4. The first set is more spread out.
4
The ages in a group are 9, 10, 10, 11, 12, 14 and an adult aged 39 joins. Find the mean and the median before and after. Which measure changes more?
Before: the total is 66, the mean is 66 ÷ 6 = 11 and the median is (10 + 11) ÷ 2 = 10.5. After: the total is 105, the mean is 105 ÷ 7 = 15 and the median is 11. The mean changes more (by 4, while the median changes by 0.5).
5
Why is the mode the only measure that works for the favourite colour of the class?
Colours are not numbers, so we cannot add them or find a middle. We can only count which colour appears most often.