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S.2 Mathematics Topic Supplementary Exercise – More about Statistical Diagrams and Graphs

Name：_______________ Date：______________

Class：___________( )

1. To organize the same set of data by different grouping methods.

2. To construct simple statistical charts including histograms, frequency polygons and curves,

cumulative frequency polygons and curves.

3. To interpret simple statistical charts including histograms, frequency polygons and curves,

cumulative frequency polygons and curves.

4. To choose appropriate diagrams/graphs to present a set of data.

5. To read information (including percentiles, quartiles, median) and frequencies from

diagrams/graphs.

6. To identify sources of deception in misleading graphs/accompanying statements.

Section A: Multiple-choice Questions

Choose the best answer for each question.

1. The following shows the ages of

members of a club.

Age Frequency

10 19 1

20 29 3

30 39 4

40 49 16

50 59 15

60 69 2

Which of the following is suitable to

present the data in the above table?

A. Histogram

B. Scatter diagram

C. Broken line graph

D. Stem-and-leaf diagram

2. The following histogram shows the

heights of some plants. The first class

interval is ‘12.6 cm – 14.4 cm’. Which

class interval has the highest frequency?

A. 19 cm 20 cm

B. 18.5 cm 20.5 cm

C. 17.6 cm 19.4 cm

D. 18.6 cm 20.4 cm

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3. The following frequency polygon shows

the thicknesses of some iron sheets. The

class boundaries of the first class interval

are 0.1 mm and 0.3 mm. Find the number

of the iron sheets with thicknesses

between 0.5 mm 1.1 mm.

A. 38

B. 31

C. 26

D. 12

4. The following frequency distribution

table shows the marks of a class of

students in a Mathematics test.

Marks Frequency

31 40 1

41 50 3

51 60 2

61 70 8

71 80 12

81 90 7

91 100 4

If the above data is presented by a

histogram, which of the following should

be obtained?

A.

B.

C.

D.

5. The following cumulative frequency

polygon shows the time taken for some

students to finish a 50 m run. Find the

number of students who spend less than

8.1 seconds.

A. 40

B. 38

C. 35

D. 32

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6. The following cumulative frequency

polygon shows the time taken for some

staff to travel to office. Find the 90th

percentile.

A. 45 minutes

B. 58 minutes

C. 69 minutes

D. 85 minutes

7. The following pie charts show the

distributions of the conduct grades of 2

classes of students.

Which of the following interpretation for

the pie charts must be true?

A. The number of students got Grade D

in S.1B is 3 times that in S.1A.

B. The number of students got Grade C

in S.1A is more than that in S.1B.

C. The 2 classes have the same number

of students.

D. The percentage of students with

Grade A in S.1A is higher than that

in S.1B.

8. The manager of a company uses the

diagram below to show the annual sales

of two brands of milk, brand A and brand

B.

Based on the diagram above, the manager

claims that the sales of milk of brand B is

twice the sales of milk of brand A.

Which of the following statements is the

best reason that the diagram is

misleading?

A. The annual sales of the other brands

are not shown in the diagram.

B. The market shares of two brands of

milk are not shown in the diagram.

C. The heights of the bars are not

proportional to the annual sales.

D. The vertical scale starts from 0.

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Section B: Short Questions

Working need not be shown.

9. The following shows the weights (in g) of 20 eggs.

65 68 58 54 60 66 70 56 62 64

68 66 65 57 52 59 60 58 61 63

Complete the following frequency distribution table.

Weight (g) Class mark (g) Class boundaries (g) Frequency

51 55

56 60

61 65

66 70

10. The following frequency distribution table shows the marks in an examination of a level of

students.

Marks 0 19 20 39 40 59 80 99

Frequency 3 8 24 89 76

(a) Find the class limits of the 4th class.

(b) A student passes the examination if he got 60 marks or above. Find the percentage of

students who failed.

11. The following histogram shows the lengths of some bean sprouts.

(a) Complete the following frequency distribution table according to the histogram.

Length (cm) 5 – 9 10 – 14 15 – 19 20 – 24

Frequency

(b) What is the number of bean sprouts with no longer than 14.5 cm?

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12. The following histogram shows the weights of a batch of spare parts. Those with weights

between 48.5 g 51.5 g are qualified. Find the percentage of qualified spare parts. (Give the

answer correct to 3 significant figures.)

13. The cumulative frequency curve shows the heights of servants in a restaurant.

(a) Find the total number of servants in the restaurant.

(b) Find the upper quartile.

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14. The frequency curves show the heights (in cm) of boys and girls in a class respectively.

Which group of students, boys or girls, are taller in general?

Section C: Long Questions

All working must be clearly shown.

15. The following shows the daily average temperatures (in C) recorded in April of a city.

8 9 8 6 12 10 7 5 4 2

8 6 9 7 6 5 7 10 7 6

6 3 5 12 2 4 8 9 11 14

Complete the following two frequency distribution tables.

Table 1

Average temperature (C) Tally Frequency

0 – 4

5 – 9

10 – 14

Table 2

Average temperature (C) Tally Frequency

0 – 2

3 – 5

6 – 8

9 – 11

12 – 14

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16. The following frequency distribution table shows the heights of a class of students.

Heights (cm) 145 149 150 154 155 159 160 164 165 169 170 174

Frequency 1 4 8 12 7 4

Construct a histogram for the data.

17. The following frequency distribution table shows the thicknesses of some books.

Thicknesses (mm) 8 10 11 13 14 16 17 19 20 22

Frequency 8 10 9 12 5

Construct a frequency polygon for the above data.

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18. The following are the frequency distribution table for the typing speeds of a group of girls

and an incomplete cumulative frequency table.

Frequency distribution table for Cumulative frequency table for

the typing speeds of a group of girls the typing speeds of a group of girls

Typing speed

(words/min) Frequency

30 39 2

40 49 4

50 59 13

60 69 8

70 79 3

(a) Complete the cumulative frequency table.

(b) Draw a cumulative frequency polygon to represent the data.

Typing speed

less than

(words/min)

Cumulative

frequency

29.5 0

39.5 2

49.5 6

59.5 19

69.5

79.5

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19. The frequency polygon shows the time spent on housekeeping in a week for some women.

The class boundaries of the 1st class interval are 1.5 hours and 4.5 hours.

(a) How many women spent less than 7.5 hours on housekeeping in a week?

(b) Find the percentage of the women who spent not less than 10.5 hours on housekeeping.

(Give the answer correct to 3 significant figures.)

20. The following is an advertisement comparing the popularities of ‘Handsome’ sunglasses and

brand X sunglasses in a marketing study:

(a) What is the difference between the number of users of ‘Handsome’ sunglasses and that

of brand X sunglasses?

(b) Explain why the diagram is misleading.