MS-Sol-EE-C11

# MS-Sol-EE-C11 - CHAPTER 11 FREQUENCY DISTRIBUTIONS EXERCISE...

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CHAPTER 11 FREQUENCY DISTRIBUTIONS EXERCISE 11.1 Section 11.1 Discrete and continuous variables (page 78) 1. (a) (i) A variable is a quantity whose value is not a constant. (ii) A quantitative variable is a variable whose possible values are numeric. (iii) A qualitative variable is a variable whose possible ‘values’ are non-numeric. (b) (i) Examples of quantitative variables: the thickness of a piece of glass, the number of patients staying in a hospital (ii) Examples of qualitative variables: colour of a flower, opinion on a new regulation 2. (a) Qualitative variables: make, colour, brake system (b) Discrete quantitative variable: valve arrangement 3. (a) A discrete variable is a quantitative variable which can take up isolated values only. A continuous variable is a quantitative variable which can take up any value within a certain range. (b) Continuous variables: (i) , (iii) , (iv) , (v) . 4. (a) male, female (b) A, B, C, D, E, F, U (c) 0, 1, 2, . . . , 40 (d) 0, 1, 2, 3, . . . (e) 9 s < time < (f) 0 m distance < 5. (a) (i) and (ii) are shown in the following table: Qualitative variables Possible classes Blood type (A) A, B, AB, O Religion (B) Catholic, Christianity, Islam, Buddhism, Others Whether a smoker (F) Smoker, Non-smoker Whether agree to ban Agree, Not agree 32

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C HAPTER 11 F REQUENCY D ISTRIBUTIONS smoking in public areas (G) 33
S ECTION 11.2 F REQUENCY T ABLES (b) (i) Discrete variable: Family size (E) (ii) Possible values: 1, 2, 3, … (c) (i) and (ii) are shown in the following table: Continuous variables Possible range Height (C) 1 m to 3 m Weight (D) 20 kg to 140 kg EXERCISE 11.2 Section 11.2 Frequency tables (page 88) 1. (a) Number of orders Frequency 40 - 49 3 50 - 59 5 60 - 69 7 70 - 79 5 80 - 89 5 90 - 99 5 Total 30 (b) The percentage frequency of the first class = 3 30 100% × = 10% 2. (a) Distance (km) Frequency 400 but under 420 6 420 but under 440 12 440 but under 460 11 460 but under 480 9 480 but under 500 9 500 but under 520 3 (b) Distance less than (km) Cumulative frequency 400 0 420 6 440 18 460 29 480 38 500 47 520 50 34

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3. (a) Class boundaries are 19.5 and 29.5. Class width = 29.5 - 19.5 = 10 (b) Class limits are 30 and 39. Class mark = 1 2 (30 + 39) = 34.5 (c) The required percentage frequency = 11 40 100% × = 27.5% (d) Speed less than Cumulative frequency Cumulative percentage frequency 19.5 0 0% 29.5 5 12.5% 39.5 13 32.5% 49.5 24 60% 59.5 36 90% 69.5 40 100% 4. (a) Class boundaries are 0 and 5. Class width = 5 - 0 = 5 (b) Class mark = 1 2 (10 + 20) = 15 Class width = 20 - 10 = 10 (c) The required number of leaves = 8 + 12 + 24 = 44 (d) The required percentage = 100% 16 + 24 + 12 + 8 16 + 24 × = % 3 2 66 5. (a) The upper class boundary of the first class = 25 + (25 - 20) = 30 (b) The lower class boundary of the second class = 30 The upper class boundary of the second class = 45 + (45 - 30) = 60 (c) The class width of the third class = 2 × (80 - 60) = 40 6. (a) As the world’s record for 100 m dash is about 9.8 seconds, therefore we assume the lower
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MS-Sol-EE-C11 - CHAPTER 11 FREQUENCY DISTRIBUTIONS EXERCISE...

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