Cambridge International Mathematics

Continuous data (Chapter 17) 361

b For girls: i median¼ 158 cm ii

For boys: i median¼ 165 cm ii

c The two distributions are similar in shape, but the boys’ heights are further right than the girls’.

The median height for the boys is 7 cm more than for the girls. They are considerably taller.

As the IQRs are nearly the same, the spread of heights is similar for each gender.

a

14

200 =7%,

CF (girls) Freq. (girls) Height (h cm) Freq. (boys) CF (boys)

5 5 1406 h< 145 4 4

15 10 1456 h< 150 10 14

30 15 1506 h< 155 20 34

60 30 1556 h< 160 26 60

80 20 1606 h< 165 40 100

90 10 1656 h< 170 60 160

98 8 1706 h< 175 30 190

100 2 1756 h< 180 10 200

so , is a

point on the boys’

cumulative

frequency graph.

(150 7)

0

10

20

30

40

50

60

70

80

90

100

140 145 150 155 160 165 170 175 180

height ( cm)h

percentiles Cumulative frequency graph of

boys’ and girls’ heights

IQR¼ 163 : 5 ¡ 153 : 7 ¼ 10 cm

IQR¼ 169 ¡ 158 ¼ 11 cm

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y:\HAESE\IGCSE01\IG01_17\361IGCSE01_17.CDR Friday, 10 October 2008 9:27:15 AM PETER