6a04_fs_01e - 4 Measures of Dispersion 4 Measures of...

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4 Measures of Dispersion 4 Measures of Dispersion Review Exercise 4 (p. 4.5) 1. (a) Amount ($) Class mark ($) Frequency 50.5 149.5 100 4 150.5 249.5 200 10 250.5 – 349.5 300 7 350.5 – 449.5 400 14 450.5 – 549.5 500 5 (b) Class interval $350.5 $449.5 has the highest frequency. (c) The required percentage of students % 5 . 12 % 100 5 14 7 10 4 5 2. (a) From the graph, 14 programmes have the viewing rate of 10% or below. 14 programmes will be subject to review. (b) For the programmes which have more than 1 million viewers, the viewing rate is greater than %, 100 000 000 5 000 000 1 i.e. 20%. From the graph, 46 programmes have the viewing rate of 20% or below. Number of programmes having more than 1 million viewers 54 46 100 3. (a) Mean income 9 7 9877 $ 9 900 88 $ 9 9600 6700 8000 7400 8500 700 25 9200 7600 6200 $ Arrange the monthly incomes in ascending order, i.e. $6200, $6700, $7400, $7600, $8000, $8500, $9200, $9600, $25 700 Median income 8000 $ (b) The median can better represent the average monthly income of the employees since the extreme data ($25 700) will greatly affect the value of the mean. 4. (a) From the graph, the median score 57 (b) From the graph, the median score 56 5. (a) Mean of data in set Y 8 9 72 ] 4 26 12 4 ) 10 ( 20 13 ) 2 ( 5 [ 9 1 Let x be the datum added in set Y . 18 90 72 1 8 ) 72 ( 10 1 x x x The required datum is 18. (b) Arrange the set of data in ascending order, i.e. 10, 2, 4, 4, 5, 12, 13, 20, 26. Median 5 If the median remains unchanged, the required datum should equal to the median. The required datum is 5. Activity Activity 4.1 (p. 4.7) 1. Mean Median Mode Athlete A 7.5 7.5 7.5 Athlete B 7.5 7.5 7.5 1
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NSS Mathematics in Action 6A Full Solutions 2
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4 Measures of Dispersion 2. Since the measures of central tendency for the two athletes are all the same, they performed equally well. 3. From the dot-plots, we observe that the scores of athlete A are more spread out. Hence, the performance of athlete B is more stable. Activity 4.2 (p. 4.27) 1. (a) Set A Set B Range 9 9 Inter-quartile range 5 5 (b) No 2. No. By inspection, set A is more dispersed. Activity 4.3 (p. 4.40) 1. English 2. (a) 6 (b) 5 3. No. We don’t know the distributions of the marks./ We don’t know how many students got higher marks than Mary in each subject. (or any other reasonable answers) 4. The dispersion of the marks of the class in each subject. Activity 4.4 (p. 4.53) 1. Measure of dispersion Data set A Data set B Data set C Range 3 3 6 Inter-quartile range 1.5 1.5 3 Standard deviation 1 1 2 2. The measures of dispersion of data set B are the same as those of data set A . 3. The measures of dispersion of data set C are twice those of data set A . Let’s Discuss Let’s Discuss (p. 4.30) No, the result of their suggested formula is always zero. Let’s Discuss (p. 4.55) (a) 40, 90 (or any other reasonable answers) (b) 65, 66 (or any other reasonable answers) Classwork Classwork (p. 4.12) Data Lower half of the data Upper half of the data (a) 2, 5, 6, 8, 12, 13 2, 5, 6 8, 12, 13 (b) 1, 5, 7, 9, 11, 14, 15 1, 5, 7 11, 14, 15 (c) 3, 1, 0, 2, 2, 4, 6, 7 3, 1, 0, 2 2, 4, 6, 7 (d) 18, 30, 10, 34, 45, 18, 24, 8, 28 8, 10, 18, 18 28, 30, 34, 45 (e) 4, 4, 1, 0, 1, 0,
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