Cambridge International Mathematics

360 Continuous data (Chapter 17)

b

Cumulative frequency graphs are very useful forcomparingtwo distributions ofunequal sizes. In such

cases we use percentiles on the vertical axis. This effectively scales each graph so that they both range from

0 to 100 on the vertical axis.

Example 5 Self Tutor

The heights of100 14-year-old girls and200 14-year-old boys were measured and the results tabled.

Frequency (girls) Height (h cm) Frequency (boys)

5 1406 h< 145 4

10 1456 h< 150 10

15 1506 h< 155 20

30 1556 h< 160 26

20 1606 h< 165 40

10 1656 h< 170 60

8 1706 h< 175 30

2 1756 h< 180 10

a Draw on the same axes the

cumulative frequency curve for both

the boys and the girls.

b Estimate for both the boys and the

girls:

i the median

ii the interquartile range (IQR).

c Compare the two distributions.

0

10

20

30

40

50

60

70

70 80 90 100 110

cumulative frequency

weight (kg)

60 120

80

6868

Cumulative frequency graph of basketballers’ weights

5656

8383

9696

median is¡»¡88kg

ci

ii

iii

iv

of ,

median kg

There are men who

weigh less than kg.

There are

men who weigh more

than kg.

of , so the

th percentile kg.

50% 80 = 40

88

20

83

80 56=24

92

85% 80 = 68

85 96

) ¼

¡

¼

¡¡ ¡¡

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Y:\HAESE\IGCSE01\IG01_17\360IGCSE01_17.CDR Monday, 20 October 2008 2:37:38 PM PETER