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The range: how spread out is the data?
Discover Mathematics P6: Term 1, Unit 7, Lessons 3–4
GoalFind the range and use it to compare how spread out two data sets are.
New words
range · the largest value minus the smallest valuespread · how far apart the values arecompare · to say how two data sets are alike and different
Explanation
Two data sets can have the same mean and look very different. The mean and the median tell us about the centre; the range tells us about the spread. The range is the largest value minus the smallest value. A small range means the values are close together. A large range means they are far apart. The range uses only two values, so one outlier can make it large even when almost all the values are close together. In that case also look at the median and at the dot plot.
ƒFormula
range = largest value − smallest value
Worked examples
Club A has six members aged 10, 11, 12, 12, 13, 14. The mean is 72 ÷ 6 = 12 and the median is 12. The range is 14 − 10 = 4. The dots are close together.
Club B has six members aged 8, 9, 10, 14, 15, 16. The mean is 72 ÷ 6 = 12 and the median is (10 + 14) ÷ 2 = 12, the same as Club A. But the range is 16 − 8 = 8, twice as big. The ages of Club B are more spread out.
A misleading range. The daily numbers of customers of a bakery are 5, 6, 6, 7, 7, 8 and 40 (a holiday). The range is 40 − 5 = 35, which makes the bakery look very unsteady. But six of the seven days are between 5 and 8. Without the holiday, the range is 8 − 5 = 3. Always ask why the range is big.
Class activity
Same mean, different spread. Make two sets of five numbers with the mean 10 but different ranges, for example by moving one number up and another down by the same amount. Compute both ranges and say which set is more spread out.
Practice
1
Find the range of 12, 7, 19, 3, 10.
19 − 3 = 16.
2
Team X scores 8, 9, 10, 11, 12 and Team Y scores 2, 6, 10, 14, 18. Both means are 10. Which team is more spread out?
Team Y. Its range is 18 − 2 = 16, while Team X has 12 − 8 = 4.
3
The heights of class A have the range 20 cm and class B the range 35 cm. What does this tell us?
The heights of class B are more spread out than those of class A.
4
The range of 15, 18, 20, 24, 42 is 27. Is it a good picture of the group?
Not really. The outlier 42 makes it big. Without 42 the range is 24 − 15 = 9.
5
Write two data sets with the mean 5 but different ranges.
For example 4, 5, 6 (range 2) and 1, 5, 9 (range 8). Both means are 5.