Page 18 - TOP CLASS MATHS T5 KSSM

Mathematics Form 5 Chapter 7 Measures of Dispersion for Grouped Data

7.2 Measures of Dispersion pg. 211 – 221
Textbook
Sukatan Serakan

SMART Notes

Midpoint of the Midpoint of the 4. Standard deviation,
1. Range = highest class − lowest class Sisihan piawai,

Titik tengah Titik tengah 2
Σfx
Julat = kelas tertinggi − kelas terendah σ = 

– x
– 2
Σf
2. Interquartile range/ Julat antara kuartil
5. The smaller the standard deviation, the more consistent
= Third quartile, Q 3 – First quartile, Q 1 is the data.

Kuartil ketiga, Q 3 – Kuartil pertama, Q 1
Semakin kecil sisihan piawai, semakin konsisten data itu.
3. Variance/ Varians, 6. Box plot
Σfx 2
σ = – x Plot kotak
2
– 2
Σf
where/ dengan keadaan
x = midpoint of the class interval
titik tengah bagi selang kelas 10 20 30 40 50 60 70 80
f = frequency
kekerapan Mass (kg)/ Jisim (kg)
–
x = mean of the data
min data
10. Determine the range and interquartile range for the following distributions. PL 3
Tentukan julat dan julat antara kuartil bagi taburan berikut.
Example
Cumulative frequency
Diameter Frequency Kekerapan longgokan
(mm) Kekerapan
50
5.1 – 8.0 4
8.1 – 11.0 9 40
11.1 – 14.0 11 30
14.1 – 17.0 12
20
17.1 – 20.0 7
10

0
5.05 8.05 11.05 14.05 17.05 20.05
Diameter (mm)

Range = Midpoint of the highest class – Midpoint of the lowest class
Julat = Titik tengah kelas tertinggi – Titik tengah kelas terendah
17.1 + 20.0 5.1 + 8.0
= –
2 2
= 18.55 – 6.55
= 12 mm
From the ogive, / Daripada ogif,
1
position of Q 1 / kedudukan Q 1: × 43 = 10.75  11
4
From the ogive, / Daripada ogif,
3
position of Q 3 / kedudukan Q 3: × 43 = 32.25  32
4
Interquartile range = Third quartile, Q 3 – First quartile, Q 1
Julat antara kuartil = Kuartil ketiga, Q 3 – Kuartil pertama, Q 1
= 15.85 – 10.45
= 5.4 mm

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