Page 25 - TOP CLASS MATHS T5 KSSM

Mathematics Form 5 Chapter 7 Measures of Dispersion for Grouped Data

(d) The table shows some statistical measures of productions by three groups of machines within six months.
Jadual di bawah menunjukkan beberapa ukuran statistik bagi penghasilan kilang oleh tiga kumpulan mesin dalam enam bulan.

Group Range (tonnes) Standard deviation
Kumpulan Julat (tan) Sisihan piawai
J 228.4 13.8
K 259.3 16.5
L 243.1 11.4

You are the production manager and you have to decide which group of machines need to be serviced.
State your suggestion and justify your choice.
Anda sebagai seorang pengurus pengeluaran dikehendaki mencadangkan kumpulan mesin yang perlu diservis. Nyatakan
cadangan anda dan justifikasikan pilihan anda.
Machines of group K need to be serviced. The standard deviation is the largest. This means that the
machines are the least consistent.
Mesin kumpulan K perlu diservis. Sisihan piawainya adalah paling besar. Ini bermakna mesin-mesin itu adalah paling tidak
konsisten.

(e) The table shows the frequency distribution of the masses of durians collected from orchards A and B.
Jadual di bawah menunjukkan taburan kekerapan jisim durian yang dikutip dari dusun A dan B.

Mass / Jisim (kg) 2.0 – 2.9 3.0 – 3.9 4.0 – 4.9 5.0 – 5.9 6.0 – 6.9
Orchard A / Dusun A 7 9 3 6 5
Orchard B / Dusun B 2 4 7 9 8
Based on the mean and standard deviation, determine which orchard has heavier and more consistent
durians. Justify your answer.
Berdasarkan min dan sisihan piawai, tentukan dusun yang mempunyai durian yang lebih berat dan konsisten. Berikan
justifikasi anda.
Orchard A / Dusun A:
Mass (kg) f x fx fx 2
Jisim (kg) – 126.5
x =
2.0 – 2.9 7 2.45 17.15 42.0175 30
= 4.217 kg
3.0 – 3.9 9 3.45 31.05 107.1225
4.0 – 4.9 3 4.45 13.35 59.4075 594.775 126.5 2

–
σ =  
5.0 – 5.9 6 5.45 32.7 178.215 30 30
6.0 – 6.9 5 6.45 32.25 208.0125 = 1.430 kg
2
Σf = 30 Σfx = 126.5 Σfx = 594.775
Orchard B / Dusun B:
Mass (kg) f x fx fx 2
Jisim (kg) – 150.5
x =
2.0 – 2.9 2 2.45 4.9 12.005 30
= 5.017 kg
3.0 – 3.9 4 3.45 13.8 47.61
4.0 – 4.9 7 4.45 31.15 138.6175 798.375 150.5 2

σ =  
–
5.0 – 5.9 9 5.45 49.05 267.3225 30 30
6.0 – 6.9 8 6.45 51.6 332.82 = 1.202 kg
Σf = 30 Σfx = 150.5 Σfx = 798.375
2
Orchard B has heavier durians because the mean is larger. The masses of the durians in orchard B are
more consistent because the standard deviation is smaller.
Dusun B mempunyai durian yang lebih berat kerana minnya lebih besar. Jisim durian di dusun B lebih konsisten kerana sisihan
piawainya lebih kecil.

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