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Mathematics Form 5 Chapter 7 Measures of Dispersion for Grouped Data

SPM Practice 7

Paper 2 (b)

1. The table shows the frequency distribution of mass, in kg, Cumulative frequency
Kekerapan longgokan
of 100 luggage in an aeroplane.
Jadual di bawah menunjukkan taburan kekerapan jisim, dalam
kg, bagi 100 bagasi di dalam sebuah kapal terbang. 100

Mass (kg) / Jisim (kg) Frequency / Kekerapan 90
7 – 11 13
12 – 16 17 80
17 – 21 28
70
22 – 26 23
27 – 31 14 60
32 – 36 5
50
(a) Based on the table, complete the table in the answer
space.
Berdasarkan jadual tersebut, lengkapkan jadual di ruang 40
jawapan.
(b) Using a scale of 2 cm to 5 kg on the horizontal axis 30
and 2 cm to 10 luggage on the vertical axis, draw an
ogive for the data. 20
Menggunakan skala 2 cm kepada 5 kg pada paksi mengufuk
dan 2 cm kepada 10 bagasi pada paksi mencancang, lukis 10
satu ogif bagi data tersebut.
(c) From the ogive drawn, determine 0
Daripada ogif yang dilukis, tentukan 6.5 11.5 16.5 21.5 26.5 31.5 36.5
(i) the range of the data, Mass (kg)/ Jisim (kg)
julat bagi data itu,
(ii) the interquartile range, (c) (i) Range / Julat = 32 + 36 – 7 + 11
julat antara kuartil, 2 2
th
(iii) the 90 percentile. = 34 – 9
= 25 kg
persentil ke-90.
(d) Any luggage which is more that 25 kg is considered as (ii) From the ogive, / Daripada ogif,
excess luggage. Find the percentage of excess luggage Q 1 = 15.0
in the aeroplane. Q 3 = 25.0
Mana-mana bagasi yang melebihi 25 kg dianggap sebagai Interquartile range / Julat antara kuartil
bagasi yang melebihi muatan. Cari peratus bagasi yang = 25.0 – 15.0
melebihi muatan di dalam kapal terbang itu. = 10 kg
Answer / Jawapan: (iii) 90 percentile / Persentil ke-90
th
(a) = 29.5 kg
Upper Cumulative (d) Number of excess luggage
Mass (kg) Frequency boundary frequency Bilangan bagasi yang melebihi muatan
Jisim (kg) Kekerapan Sempadan Kekerapan = 100 – 75
atas longgokan = 25
25
2 – 6 0 6.5 0 Percentage / Peratus = 100 × 100%
7 – 11 13 11.5 13 = 25%
12 – 16 17 16.5 30
17 – 21 28 21.5 58
22 – 26 23 26.5 81
27 – 31 14 31.5 95
32 – 36 5 36.5 100

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