Mathematics - 0FEES



Mathematics

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Multiple Choice Section

1. Which of the following is a continuous datum?

A. Length

B. Number of days

C. Quantity of paper

D. Level of the building

2. The following frequency distribution table shows the heights of a group of students. How many students are 169.5 cm high or above?

| Height (cm) | Frequency |

| 140 - 149 | 7 |

| 150 - 159 | 2 |

| 160 - 169 | 5 |

| 170 - 179 | 8 |

A. 7

B. 8

C. 13

D. 14

3. The following frequency distribution table shows the heights of 70 students. How many students are 154.5 cm high or above?

| Height (cm) | Frequency |

| 135 - 139 | 16 |

| 140 - 144 | 10 |

| 145 - 149 | 15 |

| 150 - 154 | 6 |

| 155 - 159 | 18 |

| 160 - 164 | 5 |

A. 6

B. 23

C. 29

D. 47

4. The following frequency distribution table shows the monthly salaries of the workers in a factory. Find the number of workers whose monthly salaries are less than $6 750.

| Monthly salary ($) | Frequency |

| 3 300 - 3 700 | 1 |

| 3 800 - 4 200 | 3 |

| 4 300 - 4 700 | 5 |

| 4 800 - 5 200 | 10 |

| 5 300 - 5 700 | 13 |

| 5 800 - 6 200 | 8 |

| 6 300 - 6 700 | 10 |

A. 10

B. 30

C. 40

D. 50

5. The following frequency distribution table shows the Mathematics examination marks of 50 students. What percentage of students got 59.5 or higher?

| Marks | Frequency |

| 0 - 19 | 2 |

| 20 - 39 | 7 |

| 40 - 59 | 11 |

| 60 - 79 | 14 |

| 80 - 99 | 16 |

| Total | 50 |

A. 4%

B. 18%

C. 40%

D. 60%

6. The following frequency distribution table shows the weights of a group of students. Find the class mark of the third class.

| Weight (kg) | Frequency |

| 35 - 39 | 4 |

| 40 - 44 | 7 |

| 45 - 49 | 9 |

| 50 - 54 | 13 |

A. 46 kg

B. 46.5 kg

C. 47 kg

D. 47.5 kg

7. The following frequency distribution table shows the Mathematics test marks of 45 students. Find the class width.

| Marks | Frequency |

| 20 - 35 | 2 |

| 36 - 51 | 3 |

| 52 - 67 | 3 |

| 68 - 83 | 18 |

| 84 - 99 | 19 |

A. 15 marks

B. 16 marks

C. 17 marks

D. 18 marks

8. The following frequency distribution table shows the heights of a group of students. Find the upper class boundary of the second class.

| Height (cm) | Frequency |

| 145 - 149 | 4 |

| 150 - 154 | 7 |

| 155 - 159 | 9 |

| 160 - 164 | 13 |

A. 149.5 cm

B. 150 cm

C. 154 cm

D. 154.5 cm

9. The following frequency distribution table shows the daily exercise time of a class of students. Find the lower class boundary and upper class boundary of the 8th class.

| Time (min) | Frequency |

| 1 - 15 | 5 |

| 16 - 30 | 7 |

| 31 - 45 | 3 |

| 46 - 60 | 4 |

| 61 - 75 | 2 |

| 76 - 90 | 9 |

| 91 - 105 | 2 |

| 106 - 120 | 10 |

A. Lower class boundary ( 105.5 min; upper class boundary ( 120.5 min

B. Lower class boundary ( 106 min; upper class boundary ( 120 min

C. Lower class boundary ( 91 min; upper class boundary ( 105 min

D. Lower class boundary ( 90.5 min; upper class boundary ( 105.5 min

10. The histogram shows the waiting time of passengers at a bus stop. Which class has the most passengers?

[pic]

A. I

B. II

C. III

D. IV

11. The histogram shows the high jump records of F.2A students. How many students are there in F.2A?

[pic]

A. 14

B. 40

C. 41

D. 42

12. The following frequency polygon shows the waiting time of 100 passengers at a bus stop. How many passengers are there in the class interval 18 min – 19 min?

[pic]

A. 0

B. 1

C. 2

D. 5

13. The following frequency polygon shows the heights of F.2B students. How many students are there in F.2B?

[pic]

A. 35

B. 38

C. 40

D. 42

14. The following frequency polygon shows the heights of a class of students. What percentage of students is shorter than 168.5 cm?

[pic]

A. 8%

B. 10%

C. 84%

D. 92%

15. What is the range of the following frequency polygon?

[pic]

A. 29 min

B. 30 min

C. 37 min

D. 40 min

16. The following frequency polygon shows the weights of F.2A students. Which class interval has the most students?

[pic]

A. 40.5 kg - 42.5 kg

B. 41 kg - 42 kg

C. 41.5 kg

D. 41 kg

17. The following frequency polygons show the English Language test marks of F.2A and F.2B students. If the passing mark is 60, which class has a higher passing percentage in the English Language test?

[pic]

A. Both classes have the same passing percentage in the English Language test.

B. It cannot be found.

C. F.2A

D. F.2B

18. The following figures show the amounts of pocket money David and Mary spent in a certain week. If each of them spent $120 in that week, who spent more money on Sunday?

[pic]

A. Mary

B. David

C. Both of them spent the same amount on Sunday.

D. It cannot be found.

19. The following cumulative frequency polygon shows the weights of a group of students. How many students are there?

[pic]

A. 48

B. 50

C. 75.5

D. 76

20. The following cumulative frequency curve shows the Mathematics test marks of 50 students. If 50% of the students failed the test, what is the passing mark?

[pic]

A. 37

B. 42.5

C. 48

D. 50

21. The following cumulative frequency polygon shows the weights of 50 students. How many students weigh 49 kg or above?

[pic]

A. 4

B. 32

C. 46

D. 48

22. The following cumulative frequency polygon shows the waiting time of customers in a certain fast food shop at noon. Find the number of customers whose waiting time is between 4 minutes and 6 minutes.

[pic]

A. 14

B. 26

C. 33

D. 40

23. The following cumulative frequency curve shows the lengths of tuna. Find the percentage of tuna which are shorter than 20.5 cm.

[pic]

A. 10%

B. 28%

C. 72%

D. 90%

24. The following cumulative frequency polygon shows the Mathematics examination marks of 60 students. Find the median.

[pic]

A. 45

B. 50

C. 52

D. 54

25. The following cumulative frequency polygon shows the degrees of the electricity consumed by 600 families in a certain month. Find the median.

[pic]

A. 54

B. 56

C. 150

D. 220

26. The following cumulative frequency polygon shows the Mathematics examination marks of 60 students. Find the difference between the upper quartile and the lower quartile.

[pic]

A. 37

B. 48

C. 49

D. 50

27. The following cumulative frequency polygon shows the amounts spent on snack by 600 students. Find the difference between the upper quartile and the lower quartile.

[pic]

A. $25

B. $26

C. $49

D. $50

28. The following cumulative frequency polygon shows the English examination marks of 120 candidates. If the top 15% of the students will gain awards, what is the minimum mark to gain an award?

[pic]

A. 7

B. 14

C. 65

D. 74

29. The following cumulative frequency polygon shows the monthly income of 600 families in a certain public housing estate. If the top 10% of the families have to pay double housing rent, what is the minimum monthly income of these families?

[pic]

A. $2 000

B. $36 000

C. $36 800

D. $38 000

30. The following cumulative frequency polygon shows the marks of 180 candidates in a Chinese Language examination. Find the values of P20 and P80.

[pic]

A. P20 ’ 10, P80 ’ 70

B. P20 ’ 40, P80 ’ 30

C. P20 ’ 15, P80 ’ 65

D. P20 ’ 30, P80 ’ 75

31. The following figures show the prices of two brands of washing powder. Which brand of washing powder had a rapid increase in price?

[pic]

A. Brand A

B. Brand B

C. Same

D. It cannot be found.

32. The following bar chart shows the sales of air conditioners of company A. How many times is the sales of air conditioners in 2002 to that in 2000?

[pic]

A. 2 times

B. 1.3 times

C. 1.2 times

D. 1 time

Section A(1)

1. The table below shows the distribution of the amount of pocket money of F.2B students per week.

| Pocket money ($) | Number of students |

| 50 - 149 | 5 |

| 150 - 249 | 21 |

| 250 - 349 | 10 |

| 350 - 499 | 4 |

(a) How many students have pocket money less than $149.5 per week?

(b) Find the lower class limit and the upper class limit of the second class.

(c) Find the lower class boundary and the upper class boundary of the third class.

(d) Find the class mark of the fourth class.

2. The table below shows the Mathematics quiz marks of F.2C students. (Full marks is 20.)

| Mark | Number of students |

| 1 - 5 | 3 |

| 6 - 10 | 7 |

| 11 - 15 | 18 |

| 15 - 20 | 12 |

(a) Find the class interval of the second class.

(b) Find the upper class limit of the first class.

(c) How many students have less than 5.5 marks?

(d) Find the lower class limit of the third class.

(e) How many students are there in F.2C?

3. The following table shows the heights of the girls in F.2A.

| Height (cm) | Frequency | Lower class | Upper class | Class mark (cm) |

| | |boundary (cm) |boundary (cm) | |

| 140 - 144 | 5 | 139.5 | | |

| 145 - 149 | 9 | | 149.5 | |

| 150 - 154 | 4 | | | 152 |

| 155 - 159 | 2 | | | |

(a) How many girls are there in the class?

(b) Complete the table.

4. The following histogram shows the weights of F.2A students.

[pic]

(a) Which class interval has the highest frequency?

(b) Find the number of students in the class interval 55 kg – 59 kg.

(c) How many students are there in the class interval with the lowest frequency?

5. The following histogram shows the meeting time of students and the social worker last week.

[pic]

(a) Which class interval has the lowest frequency?

(b) Find the class boundaries of the class interval with the highest frequency.

(c) How many students are there in the class interval 45.5 min – 54.5 min?

(d) How many students did the social worker meet last week?

6. The following frequency polygon shows the waiting time of 100 passengers at a bus stop.

[pic]

(a) Complete the following table.

| Waiting time (min) | Class mark (min) | Frequency |

| 3 - 5 | | |

| 6 - 8 | 7 | |

| 9 - 11 | | 30 |

| 12 - 14 | 13 | |

| 15 - 17 | | |

| 18 - 20 | | 5 |

(b) Which class interval has the highest frequency? How many people are there?

(c) How many people had to wait for 14.5 min or more?

7. The following frequency polygon shows the time spent on the Internet for F.2C students every day.

[pic]

(a) Complete the following table.

| Time spent (min) | Class mark (min) | Frequency |

| 31 - 60 | | |

| 61 - 90 | | |

| 91 - 120 | 105.5 | 17 |

(b) How many students spent less than 90.5 min on the Internet?

(c) Kenny spends 85 minutes while Leon spends 1 hour on the Internet every day. Which class intervals do they belong to respectively?

8. The following frequency polygon shows the Mathematics test marks of F.3A students.

[pic]

(a) Which class interval has the highest frequency?

(b) If a certificate is awarded to the students who got 75 marks or higher, how many students can get the certificate?

(c) If the passing mark is 45, find the number of students who failed.

9. The following frequency polygons show the amount of monthly pocket money got by youngsters in Tsuen Wan and Yuen Long respectively.

[pic]

(a) Youngsters in which district get $450 or more per month?

(b) On the whole, youngsters in which district have more pocket money?

10. The cumulative frequency polygon below shows the marks of F.2A students in a Chinese Language test.

[pic]

(a) How many students are there in F.2A?

(b) How many students got less than 55.5 marks?

(c) How many students got 75.5 marks or higher?

11. The following cumulative frequency curve shows the ages of a group of interviewees.

[pic]

(a) Find the number of interviewees whose ages are between 29.5 and 49.5.

(b) What percentage of interviewees are under 39.5 years old?

12. The following cumulative frequency polygon shows the weights of F.2D students.

[pic]

(a) How many students are there in F.2D?

(b) How many students weigh under 49 kg?

(c) Find the percentage of students who weigh 55 kg or above.

13. The cumulative frequency polygon below shows the marks of F.2 students in a Geography test.

[pic]

(a) Find the median.

(b) Find the lower quartile and the upper quartile.

14. The cumulative frequency polygon below shows the time spent on TV game for F.2 students every day.

[pic]

(a) Find the median.

(b) Find the values of (P10) and (P90).

Section A(2)

15. The following histogram shows the heights of 20 boys of the same age.

[pic]

(a) How many boys have heights less than 155 cm?

(b) As shown in the table, the price of buffet dinner of Typical Restaurant varies with customers’ heights.

| Height | Price |

| Taller than or equal to 135 cm, but shorter than 145 cm | $140 |

| Taller than or equal to 145 cm, but shorter than 155 cm | $150 |

| Taller than or equal to 155 cm, but shorter than 165 cm | $160 |

| Taller than or equal to 165 cm, but shorter than 175 cm | $170 |

| Taller than or equal to 175 cm, but shorter than 185 cm | $180 |

(i) If the above 20 boys take the buffet dinner in the restaurant, how much do they have to pay in total?

(ii) If price changes so that people who are taller than 165 cm have to pay $160 only for the dinner. How much can the boys save?

16. The following frequency polygon shows the time taken in a 60-minute test by a group of students.

[pic]

(a) How many students had finished the test 9.5 minutes before the test ended?

(b) If bonus marks will be awarded to students who finish the test within 40.5 minutes, what percentage of students can get the bonus marks?

17. The frequency polygon below shows the lengths of 200 chopsticks produced by Tai Chung Factory.

[pic]

(a) Chun Tat Factory also examines 200 chopsticks at random and the result is as follows:

| Length (cm) | Frequency |

| 19.75 - 19.85 | 13 |

| 19.95 - 20.05 | 45 |

| 20.15 - 20.25 | 79 |

| 20.35 - 20.45 | 33 |

| 20.55 - 20.65 | 21 |

| 20.75 - 20.85 | 9 |

Construct a frequency polygon according to the above table.

(b) Lucky Restaurant needs chopsticks of better quality (i.e. chopsticks of nearly the same length). Which factory would you suggest the restaurant to buy from?

18. The two frequency polygons below show the time spent on watching TV for F.2A and F.2B students every day.

[pic]

(a) How many students are there in F.2A and F.2B respectively?

(b) Which class has a more concentrated distribution?

(c) Which class has more students who spent 1 hour and 45 minutes or more on watching TV every day?

19. The following frequency curve shows the waiting time of a group of customers of Great Happy Fast Food Shop.

[pic]

(a) The owner of the fast food shop claims that the average waiting time of customers is 1.5 minutes. Is that true?

(b) Ka Ming waited for 2 minutes and 45 seconds. Did he wait too long in comparison with most of the customers?

(c) What percentage of customers waited less than 45 seconds?

20. The following cumulative frequency polygon shows the average marks of F.2A students in the final examination.

[pic]

Students with good results will be awarded a certificate of merit according to the following system:

| Average mark | Grade of merit |

| 91 - 100 | A |

| 71 - 90 | B |

(a) How many students can get grade-A certificates?

(b) How many students can get grade-B certificates?

(c) How many students do not get any certificate?

21. The following cumulative frequency polygon shows the English test marks of F.2B students.

[pic]

(a) Find the percentage of students who got 75.5 marks or above.

(b) If there are 15 students who get x marks or above, find the maximum value of x.

(c) If the top 20% students will be awarded a certificate, what is the lowest mark among them?

22. The following cumulative frequency polygon shows the weights of the boys in F.2.

[pic]

(a) According to the graph, complete the following tables.

| Weight less than | Cumulative | | Weight (pounds) | Frequency |

|(pounds) |frequency | | | |

| 100.5 | | | 96 - 100 | |

| 105.5 | | | 101 - 105 | |

| 110.5 | | | 106 - 110 | |

| 115.5 | | | 111 - 115 | |

| 120.5 | | | 116 - 120 | |

| 125.5 | | | 121 - 125 | |

| 130.5 | | | 126 - 130 | |

(b) Which class interval has the highest frequency?

(c) If the heaviest 20% of students are classified as overweight and need to be on diet, find the minimum weight among them.

23. The following cumulative frequency curves show the marks of F.2B students in a Chinese Language examination and a Mathematics examination respectively.

[pic]

(a) How many students got marks between 66 and 75 in the two examinations respectively?

(b) (i) Find the upper quartile and the lower quartile in the Chinese Language examination.

(ii) Find the upper quartile and the lower quartile in the Mathematics examination.

(iii) Hence, find the difference between the two quartiles of each examination. In which examination can you find a larger difference?

(c) If the passing marks of the two examinations are the same and there are same number of students who passed the two examinations, find the passing mark and the passing percentage. (Suppose the passing mark is less than 60.)

24. The frequency distribution table shows the results of F.2D students in Art.

| Mark | Frequency |

| 31 - 40 | 4 |

| 41 - 50 | 6 |

| 51 - 60 | 13 |

| 61 - 70 | 9 |

| 71 - 80 | 6 |

| 81 - 90 | 2 |

(a) Construct a cumulative frequency table.

| Mark less than | Cumulative frequency |

| 40.5 | |

| 50.5 | |

| 60.5 | 23 |

| 70.5 | |

| 80.5 | |

| 90.5 | |

(b) Using the result of (a), construct a cumulative frequency polygon.

(c) Find the median.

(d) If the top 20% of students is classified as grade A, what is the lowest mark need to get grade A?

25. The following cumulative frequency polygon shows the time spent on the Internet per week by 200 users.

[pic]

(a) Find, among the 200 users,

(i) the value of P40.

(ii) the value of P80.

(b) If the top 40% of users can enjoy a discount,

(i) how many users can enjoy the discount?

(ii) what is the minimum consumption in order to enjoy a discount?

26. The following cumulative frequency polygon shows the studying time per day for F.2A students.

[pic]

(a) How many students spend one to two hours on studying every day?

(b) What percentage of students spend less than half an hour on studying every day?

(c) Mr. Chan guesses that

(i) more than half of his students spend less than 1.5 hours on studying every day,

(ii) 10% or more of his students spend 2.5 hours or more on studying every day.

Is he correct?

27. The following bar chart shows the average daily sales of 3 different newspapers.

[pic]

(a) Which newspaper has the best sales?

(b) Dick claims that the sales of Banana Daily is twice the sales of West Daily.

(i) Is he correct?

(ii) Let the sales of Banana Daily be x and that of West Daily be y. Find x : y. Hence, amend Dick’s claim.

(c) Does the graph mislead readers? Explain.

28. Super Power Company and Power King Company manufacture their respective new batteries. The spokesman of Super Power Company claims that the lifetime of its new battery has increased by 80%, but the lifetime of the new battery of Power King Company has just increased by 50%. Hence, he concludes that the new battery manufactured by his company is more long-lasting. He also explains his claim with the following graph.

[pic]

(a) What is the mistake of the bar chart?

(b) What is the mistake of his claim?

Section B

29. The following histogram shows the weights of school bags of Primary 6 students in Pleasurable Primary School.

[pic]

(a) (i) According to the histogram, complete the tables below.

| Weight (pounds) |Frequency | | Weight less than (pounds) | Cumulative |

| | | | |frequency |

| 9 - 10 | | | 10 | |

| 10 - 11 | | | 11 | |

| 11 - 12 | | | 12 | |

| 12 - 13 | | | 13 | |

| 13 - 14 | | | 14 | |

| 14 - 15 | | | 15 | |

(ii) Construct a cumulative frequency polygon.

(b) Find the median.

(c) Concerning with the health of students’ backbone, the school is promoting “Lighter School Bag Campaign”. As a result, all school bags of the students are reduced by 1 pound. What is the new median?

Answer

Multiple Choice Section

1. A

∵ Measured values are continuous data.

∴ Length is a continuous datum.

2. B

Number of students whose heights are 169.5 cm or above = 8

3. B

Number of students whose heights are 154.5 cm or above ’ 18 ( 5

’ 23

4. D

Number of workers whose monthly salaries are less than $6 750

( 1 + 3 + 5 + 10 + 13 + 8 + 10

( 50

5. D

Number of students who got 59.5 or higher ( 14 ( 16

( 30

∴ The percentage[pic]

6. C

Class mark of the third class [pic]

7. B

Lower class boundary of the first class ( 19.5 marks

Upper class boundary of the first class ( 35.5 marks

Class width ’ (35.5 – 19.5) marks

’ 16 marks

8. D

Class interval of the second class is 150 cm - 154 cm.

∴ Upper class boundary of the second class is 154.5 cm.

9. A

Class interval of the 8th class is 106 min - 120 min.

∴ Lower class boundary of the 8th class ’ 105.5 min

Upper class boundary of the 8th class ’ 120.5 min

10. A

The rectangular bar of class I is the highest, so class I has the most passengers.

11. C

Number of students ( 6 + 12 + 15 + 6 + 2

’ 41

12. B

Class mark of that class [pic]min

[pic]min

∴ According to the figure, there is 1 passenger.

13. C

Number of students ( 2 + 7 + 2 + 13 + 6 + 5 + 5

’ 40

14. D

Number of students who is shorter than 168.5 cm [pic]

Number of students in the class [pic]

∴ The percentage [pic]

15. A

[pic]

The range is the difference between the maximum value and the minimum value of the data.

∵ Maximum value ( 50 min

Minimum value ( 21 min

∴ Range ( (50 ( 21) min

( 29 min

16. B

The second class has the most students, i.e. the class interval 41 kg – 42 kg.

17. C

Percentage of students passed in F.2A [pic]

Percentage of students passed in F.2B [pic]

∴ F.2A has a higher passing percentage in the English Language test.

18. A

Amount of pocket money David spent on Sunday

[pic]

Amount of pocket money Mary spent on Sunday [pic]

∴ Mary spent more money on Sunday.

19. B

Number of students ’ 50

20. C

[pic]

Number of students who failed the test [pic]

∴ According to the graph, the passing mark is 48.

21. A

[pic]

Number of students who weigh 49 kg or above

[pic]

22. B

[pic]

Number of customers whose waiting time is between 4 minutes and 6 minutes

[pic]

23. C

[pic]

The total number of tuna is 250 000.

There are 180 000 tuna which are shorter than 20.5 cm.

∴ The percentage [pic]

24. D

[pic]

From the graph,

∵ the corresponding cumulative frequency [pic]

∴ Median [pic]

25. A

[pic]

From the graph,

∵ the corresponding cumulative frequency [pic]

∴ Median [pic]

26. D

[pic]

From the graph,

∵ the cumulative frequency for Q1 [pic]

∴ [pic]

∵ the cumulative frequency for Q3 [pic]

∴ [pic]

∴ Difference between the upper quartile and the lower quartile ’ 64 – 14

’ 50

27. C

[pic]

From the graph,

∵ the cumulative frequency for Q1 [pic]

∴ [pic]

∵ the cumulative frequency for Q3 [pic]

∴ [pic]

∴ Difference between the upper quartile and the lower quartile ’ $66 – $17

’ $49

28. D

[pic]

From the graph,

∵ the corresponding cumulative frequency [pic]

∴ Minimum mark ’ 74

29. C

[pic]

From the graph,

∵ the corresponding cumulative frequency [pic]

∴ Minimum monthly income ( $36 800

30. A

[pic]

From the graph,

∵ the cumulative frequency for P20 [pic]

∴ [pic]

∵ the cumulative frequency for P80 [pic]

∴ [pic]

31. A

Brand A washing powder had a rapid increase in price. It is because the price of Brand A increases from $30 to $40 within 2 months while that of Brand B increases the same amount in 8 months.

32. C

Sale of air conditioners in 2002 = 60 000

Sale of air conditioners in 2000 = 50 000

∴ The sales of air conditioners in 2002 is [pic]times ( 1.2 times of that in 2000.

Section A(1)

1. (a) There are [pic].

(b) Lower class limit = [pic], upper class limit = [pic]

(c) Lower class boundary = [pic], upper class boundary = [pic]

(d) Class mark = [pic]

= [pic]

2. (a) The class interval is [pic].

(b) Upper class limit = [pic]

(c) There are [pic]who have less than 5.5 marks.

(d) Lower class limit = [pic]

(e) Number of students = [pic]

= [pic]

3. (a) Number of girls = [pic]

= [pic]

(b)

| Height (cm) | Frequency | Lower class | Upper class | Class mark (cm) |

| | |boundary (cm) |boundary (cm) | |

| 140 - 144 | 5 | 139.5 | 144.5 | 142 |

| 145 - 149 | 9 | 144.5 | 149.5 | 147 |

| 150 - 154 | 4 | 149.5 | 154.5 | 152 |

| 155 - 159 | 2 | 154.5 | 159.5 | 157 |

4. (a) The class interval [pic] has the highest frequency.

(b) Number of students = [pic]

(c) Number of students = [pic]

5. (a) The class interval [pic]has the lowest frequency.

(b) Lower class boundary = [pic], upper class boundary = [pic]

(c) Number of students = [pic]

(d) Number of students = [pic]

= [pic]

6. (a)

| Waiting time (min) | Class mark (min) | Frequency |

| 3 - 5 | 4 | 17 |

| 6 - 8 | 7 | 19 |

| 9 - 11 | 10 | 30 |

| 12 - 14 | 13 | 22 |

| 15 - 17 | 16 | 7 |

| 18 - 20 | 19 | 5 |

(b) The class interval [pic] has the highest frequency. There are [pic] people.

(c) Number of people = [pic]

= [pic]

7. (a)

| Time spent (min) | Class mark (min) | Frequency |

| 31 - 60 | 45.5 | 6 |

| 61 - 90 | 75.5 | 14 |

| 91 - 120 | 105.5 | 17 |

(b) Number of people = [pic]

= [pic]

(c) Kenny belongs to the class interval [pic], Leon belongs to the class interval [pic].

8. (a) The class interval [pic] has the highest frequency.

(b) There are [pic] who can get the certificate.

(c) Number of students who failed = [pic]

9. (a) Yuen Long

(b) Tsuen Wan

10. (a) There are [pic] in F.2A.

(b) There are 18 students who got less than 55.5 marks.

(c) Number of students who got 75.5 marks or higher = [pic]

= [pic]

11. (a) Number of interviewees whose ages are between 29.5 and 49.5

= [pic]

= [pic]

(b) Number of interviewees who are under 39.5 years old = 68

Total number of interviewees = 100

∴ The percentage = [pic]

= [pic]

12. (a) There are [pic] in F.2D.

(b) There are [pic] who weigh under 49 kg.

(c) Number of students who weigh 55kg or above

= 40 ( 24

= 16

∴ The percentage = [pic]

= [pic]

13. (a) ∵ The cumulative frequency for Q2[pic],

∴ [pic]

(b) ∵ The cumulative frequency for Q1[pic],

∴ [pic]

∵ The cumulative frequency for Q3[pic],

∴ [pic]

14. (a) ∵ The cumulative frequency for Q2[pic],

∴ [pic]

(b) ∵ The cumulative frequency for P10[pic],

∴ [pic]

(c) ∵ The cumulative frequency for P90[pic],

∴ [pic]

Section A(2)

15. (a) Number of boys = [pic]

= [pic]

(b) (i) Total amount = [pic]

= [pic]

(ii) Amount saved = [pic]

= [pic]

16. (a) Number of students = [pic]

= [pic]

(b) Number of students = [pic]

= [pic]

Total number of students = [pic]

= [pic]

∴ The percentage = [pic]

= [pic]

17. (a)

[pic]

(b) Tai Chung Factory

18. (a) Number of students in F.2A = [pic]

= [pic]

Number of students in F.2B = [pic]

= [pic]

(b) [pic] has a more concentrated distribution.

(c) In F.2A, the required number of students = [pic]

= [pic]

In F.2B, the required number of students = 7

∴ F.2B has more students who spent 1 hour and 45 minutes or more on watching TV every day.

19. (a) He is wrong. From the graph, most of the customers waited more than 1.5 minutes, so the average waiting time must be more than 1.5 minutes.

(b) Yes.

(c) Number of customers who waited less than 45 seconds = 6

Total number of customers = [pic]

= [pic]

∴ The percentage = [pic]

= [pic]

20. (a) Number of students who get grade-A certificates

= [pic]

= [pic]

(b) Number of students who get grade-B certificates

= [pic]

= [pic]

(c) Number of students who do not get any certificate = [pic]

21. (a) Number of students who got 75.5 marks or above

= [pic]

= [pic]

∴ The percentage = [pic]

= [pic]

(b) The maximum value of x is [pic].

(c) The top 8 students can get the certificates, i.e. 32 students cannot get the certificates.

∴ The lowest mark is [pic].

22. (a)

| Weight less than | Cumulative | | Weight (pounds) | Frequency |

|(pounds) |frequency | | | |

| 100.5 | 7 | | 96 - 100 | 7 |

| 105.5 | 30 | | 101 - 105 | 23 |

| 110.5 | 47 | | 106 - 110 | 17 |

| 115.5 | 72 | | 111 - 115 | 25 |

| 120.5 | 90 | | 116 - 120 | 18 |

| 125.5 | 98 | | 121 - 125 | 8 |

| 130.5 | 100 | | 126 - 130 | 2 |

(b) The class interval [pic] has the highest frequency.

(c) The minimum weight is [pic].

23. (a) Number of students who got 66-75 in the Chinese Language examination

= [pic]

= [pic]

Number of students who got 66-75 in the Mathematics examination

= [pic]

= [pic]

(b) (i) ∵ The cumulative frequency for Q3[pic],

∴ [pic]

∵ The cumulative frequency for Q1[pic],

∴ [pic]

(ii) ∵ The cumulative frequency for Q3[pic],

∴ [pic]

∵ The cumulative frequency for Q1[pic],

∴ [pic]

(iii) The difference between the two quartiles in the Chinese Language examination

= 82 ( 65.5

= [pic]

The difference between the two quartiles in the Mathematics examination

= 84(59.5

= [pic]

∴ [pic]

(c) Passing mark = [pic]

Passing percentage = [pic]

= [pic]

= [pic]

24. (a)

| Mark less than | Cumulative frequency |

| 40.5 | 4 |

| 50.5 | 10 |

| 60.5 | 23 |

| 70.5 | 32 |

| 80.5 | 38 |

| 90.5 | 40 |

(b)

[pic]

(c) ∵ The cumulative frequency for Q2[pic],

∴ [pic]

(d) Number of grade A students = [pic]= 8

∴ The lowest mark = [pic]

25. (a) (i) ∵ The cumulative frequency for P40[pic],

∴ [pic]

(ii) ∵ The cumulative frequency for P80[pic],

∴ [pic]

(b) (i) Number of users = [pic] = [pic]

(ii) 80 users can enjoy the discount.

∴ The minimum consumption = [pic]

26. (a) Number of students = [pic] = [pic]

(b) Number of students = [pic]

∴ The percentage = [pic]

= [pic]

(c) (i) Number of students who spend less than 1.5 hours on studying

= 17 (i.e. less than 50%)

∴ [pic]

(ii) Number of students who spend 2.5 hours or more on studying = [pic]

= [pic]

The percentage = [pic]

= [pic]

∴ [pic]

27. (a) Banana Daily

(b) (i) He is wrong.

(ii) [pic]

[pic]

∴ [pic]

The sales of Banana Daily is one-third more than that of West Daily.

(c) Yes, it is because the scale of the vertical axis does not start from 0.

28. (a) The widths of the two bars are different.

(b) The new battery with a greater percentage increase in lifetime may not have a longer lifetime. If the old battery of Super Power Company has a shorter lifetime than that of Power King Company, the lifetime of the new battery of Super Power Company may still be shorter than that of Power King Company even though the percentage increase is higher.

Section B

29. (a) (i)

| Class boundaries of the | Frequency | | Weight less than (pounds) | Cumulative |

|weight (pounds) | | | |frequency |

| 9 - 10 | 2 | | 10 | 2 |

| 10 - 11 | 7 | | 11 | 9 |

| 11 - 12 | 15 | | 12 | 24 |

| 12 - 13 | 32 | | 13 | 56 |

| 13 - 14 | 21 | | 14 | 77 |

| 14 - 15 | 3 | | 15 | 80 |

(ii)

[pic]

(c) ∵ The cumulative frequency for Q2[pic],

∴ [pic]

(d) New median = (12.5 ( 1) pounds

= [pic]

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