Page 110 - Mathematics Coursebook

10.3 Comparing distributions

10.3 Comparing distributions

You can use an average and the range to summarise a set of data.
You need to choose which average to use: the mode, the median or the mean. An average is a

"e range measures the spread of the data. representative or
typical value.
You can also use the same statistics to compare two sets of data.
Worked example 10.3

A slimming club recorded the masses (in kilograms) of eight men Men: 65, 79, 68, 72, 77, 77, 81, 67
and six women.
Calculate the mean and the range of each set of data and use Women: 68, 52, 47, 49, 50, 58
them to compare the two sets.

+
+
+
+
+
+
+
65 79 68 72 77 77 81 67
The mean for the men is 73.25 kg.
8
586
= 8 = 73.25

68 52 47 49 50 58 324
+
+
+
+
+
The mean for the women is 54 kg. = = 54
6 6
On average the men are 19.25 kg heavier than the women. 73.25 − 54 = 19.25
The range for the men is 16 kg. 81 − 65 = 16
The range for the women is 21 kg. 68 − 47 = 21
The women’s masses are more varied than the men’s. 21 is greater than 16.
In the example you compared:
t the average of each group, using the mean (you could also use the median for this)
t the variation within each group, using the range.
) Exercise 10.3
1 A primary PE teacher measured the Group A: 84 cm, 73 cm, 89 cm, 80 cm, 77 cm
heights of two groups of young children. Group B: 77 cm, 85 cm, 75 cm, 69 cm, 82 cm, 67 cm, 72 cm
The results are shown on the right.
a Work out the median height for each group.
b Use the medians to state which group is taller, on average.

2 The test marks of two groups of students are shown on
the right. Maths: 77, 89, 75, 80, 80, 91, 78, 76, 76, 76
a Work out the range for each test. Science: 72, 78, 77, 87, 86, 79, 66, 75
b Which test has a greater variation in the marks?
3 In the 2010 football World Cup, Spain won and Brazil was knocked out Spain: 0, 2, 2, 1, 1, 1, 1
in the quarter finals. The numbers of goals they scored in their matches

are shown on the right. Brazil: 2, 3, 0, 3, 1
Work out the mean scores and state which team scored more goals per
match, overall.

10 Averages 109