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24 + 22 (e)
(b) × 100% Cumulative
7 + 45 + 24 + 22 + 8 + 4 frequency
= 46 × 100% 80
110
= 41.8% [2] 70
(c) Mean
15 × 7 + 25 × 45 + 32.5 × 24 + 40 × 60
22 + 50 × 8 + 57.5 × 4 50
=
110 40
= 3520
110 30
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= 32 [4] 20
11
10
0
150 155 160 165 170 175 180 185 190
Height (cm)
142 145 151.5 162 175
Height (cm) [3]
[5] (f) (i) 170 – 171 [1]
(ii) 174.5 – 163.5 = 11

12 (a) Height (cm) Frequency 13 (a) City A: 24 [2]
150 < h ≤ 155 5 City B: 44 [2]
(b) 20 [1]
155 < h ≤ 165 15 (c) (i) 42 – 44 [1]
165 < h ≤ 170 18 (ii) 30 [1]
(d) (i) 58 [1]
170 < h ≤ 175 24 (ii) 62 [1]
175 < h ≤ 185 6 (e) 11, 9, 9, 8, 6, 4, 2, 1 [3]
1832.5
185 < h ≤ 190 2 14 (a) 40 = 45.8125 minutes [4]

[2] (b) (i) 5, 11, 33, 40 [2]
11772.5 (ii) Correct curve or ruled polygon
(b) = 168.18 [4]
70 Cumulative
(c) 170 < h ≤ 175 [1] frequency
(d)
Height (cm) Cumulative frequency
40
h ≤ 155 5
h ≤ 165 20
30
h ≤ 170 38
h ≤ 175 62
h ≤ 185 68 20

h ≤ 190 70
[2] 10

0
30 35 40 45 50 55 60
Time (t mins)
[3]
(iii) Median: 47 – 48
Interquartile range: 49 – 43.5 = 5.5 [3]

Cambridge IGCSE
TM
182 Ace Your Mathematics

Answers.indd 182 15/03/2022 11:08 AM