Page 15 - TOP CLASS MATHS T5 KSSM

Mathematics Form 5 Chapter 7 Measures of Dispersion for Grouped Data
9. For each of the following frequency tables, construct an ogive by using
suitable scales. Hence, determine. PL 4
th
• First quartile, Q 1 = 25 percentile, P 25
Bagi setiap jadual kekerapan berikut, bina ogif dengan menggunakan skala yang sesuai. Kuartil pertama, Q 1 = Persentil ke-25
Seterusnya, tentukan • Median, Q 2 = 50 percentile, P 50
th
Median, Q 2 = Persentil ke-50
(i) the first quartile, / kuartil pertama, th
• Third quartile, Q 3 = 75 percentile, P 75
(ii) the median, Percentiles Kuartil ketiga, Q 3 = Persentil ke-75
(iii) the third quartile, / kuartil ketiga, Persentil
(iv) the 60 percentile. / persentil ke-60. NOTES
th
Example
Mass (kg) 41 – 45 46 – 50 51 – 55 56 – 60 61 – 65 66 – 70 71 – 75
Jisim (kg)
Frequency 6 9 13 18 15 14 5
Kekerapan

Upper Cumulative
Mass (kg) Frequency boundary frequency
Jisim (kg) Kekerapan • The position of first quartile, Q 1
Sempadan atas Kekerapan longgokan = 1 × total frequency
4
36 – 40 0 40.5 0 Kedudukan kuartil pertama, Q 1
1
= × jumlah kekerapan
4
41 – 45 6 45.5 6 • The position of median, Q 2
= 1 × total frequency
46 – 50 9 50.5 15 2
Kedudukan median, Q 2
1
51 – 55 13 55.5 28 = 2 × jumlah kekerapan
• The position of third quartile, Q 3
56 – 60 18 60.5 46 = 3 × total frequency
4
61 – 65 15 65.5 61 Kedudukan kuartil ketiga, Q 3
3
= × jumlah kekerapan
4
66 – 70 14 70.5 75 • The position of n percentile, P n
th
= n × total frequency
71 – 75 5 75.5 80 100
Kedudukan persentil ke-n
= n × jumlah kekerapan
100
Cumulative frequency
Kekerapan longgokan 1
(i) × 80 = 20
4
From the ogive,
80
Daripada ogif,
Q 1 = 52.5 kg
70 1
(ii) × 80 = 40
2
60 From the ogive,
Daripada ogif,
Q 2 = 59.0 kg
50
3
(iii) × 80 = 60
4
40
From the ogive,
Daripada ogif,
30 Q 3 = 65.0 kg
(iv) 60 × 80 = 48
20 100
From the ogive,
Daripada ogif,
10 P 60 = 61.0 kg

0
40.5 45.5 50.5 55.5 60.5 65.5 70.5 75.5
Mass (kg)
Jisim (kg)

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