Full Solution 2A Chapter 3



7 Simple Statistical Diagrams and Graphs (II)

Activity

Activity 7.1 (p. 7.6)

1. They are the same.

2. (a) histogram

(b) frequency polygon

Activity 7.2 (p. 7.21)

1. (a) 2

(b) (2) + (5) = 7

(c) (7) + (11) = 18

(d) (18) + (9) = 27

(e) (27) + (3) = 30

|2. |Pulse rate less than (beats |Number of students |

| |per minute) | |

| |109.5 |0 |

| |114.5 |2 |

| |119.5 |7 |

| |124.5 |18 |

| |129.5 |27 |

| |134.5 |30 |

Activity 7.3 (p. 7.39)

1. Yes, from the pie chart, around[pic]of the students spend between $15 – $19 on lunch.

2. No, from the cumulative frequency polygon, 84% of the students spend less than $24.5 on lunch.

Activity 7.4 (p. 7.44)

1. (a) 1 : 2 : 3

(b) 6 : 7 : 8

(c) Yes, because the lengths of the bars are not proportional to the sales.

(d) No, the difference in sales is not big.

2. (a) 2 : 3 : 4

(b) Yes, the areas of the eggs are not proportional to the egg production.

Classwork

Classwork (p. 7.29)

|1. |Height below (cm) |Number of students |Percentage of |

| | | |students |

| |149.5 |16 |40% |

| |157 |30 |75% |

| |160.5 |34 |85% |

2. (a) 149.5 cm is the 40th percentile of the heights of

students.

(b) The 75th percentile of the heights of students is

157 cm.

(c) The 85th percentile of the heights of students is

160.5 cm.

Classwork (p. 7.40)

(a) scatter diagram

(b) stem-and-leaf diagram

(c) broken-line graph

(d) pie chart

(e) histogram or frequency polygon

Quick Practice

Quick Practice 7.1 (p. 7.9)

(a) The required class marks are 75.5, 125.5, 175.5, 225.5, 275.5 and 325.5.

|(b) |Class mark |Frequency |

| |25.5 |0 |

| |75.5 |7 |

| |125.5 |10 |

| |175.5 |12 |

| |225.5 |6 |

| |275.5 |3 |

| |325.5 |2 |

| |375.5 |0 |

[pic]

Quick Practice 7.2 (p. 7.11)

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

| |(min) |(min) | |

| |1 – 3 |2 |0 |

| |4 – 6 |5 |5 |

| |7 – 9 |8 |8 |

| |10 – 12 |11 |7 |

| |13 – 15 |14 |3 |

| |16 – 18 |17 |2 |

| |19 – 21 |20 |0 |

| | |Total |25 |

(b) There are 25 customers in total.

(c) The class interval 7 min – 9 min has the highest

frequency. There are 8 customers in this class interval.

Quick Practice 7.3 (p. 7.13)

(a) [pic]

(b) Since the position of the frequency polygon of the weights of 100 pigs in farm B is to the right of that of farm A, the pigs in farm B are heavier than those in farm A in general.

(c) In farm B,

the number of pigs with weight 99.5 kg or above

[pic]

∴ The required percentage[pic]

Quick Practice 7.4 (p. 7.15)

(a) From the frequency curve of S1 athletes, the class boundaries of the last class interval are 3.305 m and 3.405 m. Therefore, there are no records longer than 3.405 m in S1.

(b) From the frequency curve of S2 athletes, the class boundaries of the first class interval are 2.905 m and 3.005 m. Therefore, there are no records shorter than 2.905 m in S2.

(c) From the frequency curves, S1 athletes have more records lying between 2.955 m and 3.155 m.

(d) From the frequency curves, S2 athletes have more records lying between 3.155 m and 3.355 m.

(e) Since the frequency curve of the records of S2 athletes lies to the right of that of S1 athletes, the performance of S2 athletes is better in general.

Quick Practice 7.5 (p. 7.23)

|(a) |Pocket money less than ($) |Cumulative frequency |

| |200.5 |0 |

| |300.5 |10 |

| |400.5 |50 |

| |500.5 |120 |

| |600.5 |170 |

| |700.5 |190 |

| |800.5 |200 |

(b) [pic]

Quick Practice 7.6 (p. 7.25)

[pic]

(a) From the graph, 17 students have less than 60 marks. So, 17 students have failed the test.

(b) From the graph, 9 students have less than 50 marks. So, the passing mark is 50.

Quick Practice 7.7 (p. 7.27)

[pic]

(a) From the graph, there are 30 employees in the company.

(b) From the graph, 10 employees have a monthly salary less than $8000.

(c) From the graph, 20 employees have a monthly salary less than $12 000.

∴ Number of employees having a monthly salary of $12 000 or more

[pic]

Quick Practice 7.8 (p. 7.32)

(a) [pic]

(i) The cumulative frequency that corresponds to the lower quartile

= 25% ( total frequency

= 25% ( 80

= 20

From the graph, the amount of sleep that corresponds to a cumulative frequency of 20 is 7.4 h. Thus, the lower quartile =[pic]

(ii) The cumulative frequency that corresponds to the median

= 50% ( total frequency

= 50% ( 80

= 40

From the graph, the amount of sleep that corresponds to a cumulative frequency of 40 is 8.2 h. Thus, the median =[pic]

(iii) The cumulative frequency that corresponds to the upper quartile

= 75% ( total frequency

= 75% ( 80

= 60

From the graph, the amount of sleep that corresponds to a cumulative frequency of 60 is 9.1 h. Thus, the upper quartile =[pic]

(b) [pic]

(i) From the graph, 10 students sleep less than 7 hours a day.

∴ Percentage of students who sleep less than

7 hours a day

[pic]

(ii) From the graph, 76 students sleep less than

10.5 hours a day.

∴ Percentage of students who sleep at least

10.5 hours a day

[pic]

Quick Practice 7.9 (p. 7.33)

[pic]

(a) From the graph, the 60th percentile =[pic]

(b) From the graph, the 90th percentile =[pic]

(c) The lowest blood pressure for a patient to undergo further tests is the 80th percentile.

From the graph, the 80th percentile =[pic]

∴ The lowest blood pressure for a patient to undergo further tests is 145 mmHg.

Quick Practice 7.10 (p. 7.41)

(a) Histogram:

[pic]

Pie chart:

[pic]

(b) Histogram should be used. It can show the frequency of each class mark for each class interval.

(c) No. A bar chart is often used to present discrete data. Areas of flats belong to continuous data.

Quick Practice 7.11 (p. 7.42)

(a) Broken-line graph should be used because it can show the trend of the data.

(b) [pic]

Quick Practice 7.12 (p. 7.47)

(a) The vertical axis of the first graph starts from zero while that of the second graph starts from 350. Besides, the scale of the vertical axis is changed from 200 000 per 10 divisions to 100 000 per 10 divisions.

(b) It gives readers an impression that the increase of customers is significant.

Quick Practice 7.13 (p. 7.48)

(a) From the diagram, the required ratio = 2 : 4

= [pic]

(b) No, the ratio of the areas of the magazines drawn for 2007 and 2008 in the diagram is not the same as that found in (a).

(c) Yes, the diagram misleads readers because the ratio of the areas of the magazines drawn for 2007 and 2008 is not 1 : 2.

Further Practice

Further Practice (p. 7.16)

|1.(a) |Lifetime (h) |Tally |Class mark (h) |Frequency |

| |85 – 89 |//// |87 |4 |

| |90 – 94 |//// // |92 |7 |

| |95 – 99 |//// ////|97 |9 |

| |100 – 104 |//// |102 |4 |

| |105 – 109 |// |107 |2 |

(b) The class interval 95 h – 99 h has the highest frequency.

(c)

[pic]

(d) Number of batteries that have lifetimes shorter than

89.5 hours

= 2 + 4

= 6

∴ The required percentage

=[pic]

=[pic] (cor. to the nearest integer)

2.

[pic]

3. Since the frequency curve of the time spent by S2A students lies to the right of that of S2B students, S2A students spend more time on doing their homework in general.

Further Practice (p. 7.27)

|(a) |Age less than |Cumulative frequency |

| |35.5 |0 |

| |40.5 |5 |

| |45.5 |17 |

| |50.5 |40 |

| |55.5 |56 |

| |60.5 |60 |

(b)

[pic]

(c) (i) From the graph,

the number of candidates of age 53 or above

[pic]

[pic]

(ii) From the graph, 29 candidates are of age below 48.

∴ [pic]

Further Practice (p. 7.34)

[pic]

1. The cumulative frequency that corresponds to the 40th percentile

= 40% ( 50

= 20

From the graph, the weight that corresponds to a cumulative frequency of 20 is 115 g.

∴ The 40th percentile =[pic]

The cumulative frequency that corresponds to the 80th percentile

= 80% ( 50

= 40

From the graph, the weight that corresponds to a cumulative frequency of 40 is 130 g.

∴ The 80th percentile =[pic]

The cumulative frequency that corresponds to the median

= 50% ( 50

= 25

From the graph, the weight that corresponds to a cumulative frequency of 25 is 119 g.

∴ Median =[pic]

2. From the graph,

number of rats of weight less than 115 g = 20

number of rats of weight more than 145 g = 1

∴ Percentage of rats with abnormal weight one month

after the experiment

[pic]

Exercise

Exercise 7A (p. 7.17)

Level 1

|1. |(a) |Weight (kg) |2.1 |

| | | |– |

| | | |2.5 |

| |30 – 39 |34.5 |0 |

| |40 – 49 |44.5 |7 |

| |50 – 59 |54.5 |14 |

| |60 – 69 |64.5 |15 |

| |70 – 79 |74.5 |6 |

| |80 – 89 |84.5 |4 |

| |90 – 99 |94.5 |4 |

| |100 – 109 |104.5 |0 |

[pic]

5. (a) The class boundaries of the first class interval are $49.5 and $99.5.

The class width[pic]

(b) The class interval $250 – $299 has the highest frequency.

(c) Number of customers spent less than $199.5

[pic]

(d) Number of customers spent more than or equal to $299.5

[pic]

Level 2

|6. |(a) |Scores |90 – |

| | | |99 |

| | | |Restaurant A |Restaurant B |

| | |45 – 49 |7 |0 |

| | |50 – 54 |10 |5 |

| | |55 – 59 |22 |12 |

| | |60 – 64 |35 |24 |

| | |65 – 69 |18 |32 |

| | |70 – 74 |7 |20 |

| | |75 – 79 |0 |7 |

(c) From the frequency curves, restaurant A has between 57 and 67 customers on most days.

10. (a) Number of students in S2A

[pic]

Number of students in S2B

[pic]

(b) Number of students in S2A who can do 20 push-ups in less than 60.5 s

[pic]

Number of students in S2B who can do 20 push-ups in less than 60.5 s

[pic]

(c) Number of students in S2A who take 80.5 s or more to do 20 push-ups

[pic]

∴ The required percentage[pic]

Number of students in S2B who take 80.5 s or more to do 20 push-ups

[pic]

∴ The required percentage[pic]

(d) Since more students in S2B can do 20 push-ups in less than 60.5 s and less students in S2B take 80.5 s or more to do 20 push-ups, S2B students is better at doing push-ups.

Exercise 7B (p. 7.34)

Level 1

1. [pic]

(a) From the graph, 7 students have scores less than 20.5. So, 7 students have failed the fitness test.

(b) From the graph, 20 students have scores less than 28. So, the passing score is 28.

2. [pic]

(a) From the graph, there are 40 students in the group.

(b) From the graph,

number of students shorter than 164.5 cm[pic]

(c) From the graph, 11 students are shorter than

159.5 cm.

∴ Number of students who are 159.5 cm or

taller

[pic]

3. [pic]

(a) From the graph,

number of patients with a blood pressure lower than 130 mmHg[pic]

(b) Number of patients with a blood pressure above

130 mmHg

= 50 – 12

= 38

∴ Percentage of patients who suffer from high blood pressure

　 [pic]

　 [pic]

4. (a) [pic]

(i) The cumulative frequency that corresponds to the median

= 50% ( 40

= 20

From the graph, the marks that corresponds to a

cumulative frequency of 20 is 13.

∴ Median[pic]

(ii) The cumulative frequency that corresponds to the upper quartile

= 75% ( 40

= 30

From the graph, the marks that corresponds to a

cumulative frequency of 30 is 17.

∴ Upper quartile[pic]

(iii) The cumulative frequency that corresponds to the lower quartile

= 25% ( 40

= 10

From the graph, the marks that corresponds to a

cumulative frequency of 10 is 10.

∴ Lower quartile[pic]

(b) From the graph, 26 students obtain below 15 marks in the quiz.

∴ Percentage of students who fail the quiz

[pic]

5. [pic]

(a) From the graph, there are 50 students in the group.

(b) (i) The cumulative frequency that corresponds to

the 30th percentile

= 30% ( 50

= 15

From the graph, the weight that corresponds to a cumulative frequency of 15 is 43.5 kg.

∴ The 30th percentile[pic]

(ii) The cumulative frequency that corresponds to the 60th percentile

= 60% ( 50

= 30

From the graph, the weight that corresponds to a cumulative frequency of 30 is 49 kg.

∴ The 60th percentile[pic]

(c) From the graph, 47 students are below 57 kg.

∴ Percentage of students who are 57 kg or above

[pic]

|6. (a) |Diameter less than (cm) |Cumulative frequency |

| |39.5 |0 |

| |44.5 |9 |

| |49.5 |17 |

| |54.5 |25 |

| |59.5 |35 |

| |64.5 |38 |

| |69.5 |40 |

(b)

[pic]

Level 2

7. [pic]

(a) From the graph, 7 applicants are shorter than 160 cm and 14 applicants are shorter than 166 cm.

∴ Number of applicants between 160 cm and

166 cm

[pic]

(b) From the graph, 10 applicants are shorter than

163 cm.

∴ Percentage of applicants who do not meet the requirement

[pic]

[pic]

(c) Number of applicants who are considered for the special team

= 50 ( 30%

= 15

From the graph, 15 applicants are 175 cm or taller.

∴ The minimum height requirement for this team is 175 cm.

8. [pic]

(a) The cumulative frequency that corresponds to the lower quartile

= 25% ( 40

= 10

From the graph, the length that corresponds to a cumulative frequency of 10 is 39.5 cm.

∴ Lower quartile[pic]

The cumulative frequency that corresponds to the median

= 50% ( 40

= 20

From the graph, the length that corresponds to a cumulative frequency of 20 is 41.8 cm.

∴ Median[pic]

The cumulative frequency that corresponds to the upper quartile

= 75% ( 40

= 30

From the graph, the length that corresponds to a cumulative frequency of 30 is 44.2 cm.

∴ Upper quartile[pic]

(b) From the graph, the number of babies shorter than

40 cm is 12.

∴ Number of babies of length below standard[pic]

(c) Number of babies regarded as above standard

[pic]

From the graph, 2 babies have length 50 cm or longer.

∴ The minimum length to be considered above standard is 50 cm.

9. [pic]

(a) From the graph, 6 students with IQ scores below 100 and 25 students with IQ scores below 120.

∴ Percentage of students with IQ scores between 100 and 120

[pic]

(b) From the graph, the cumulative frequency that corresponds to a score of 125 = 30

∴ Percentage of students obtain IQ scores higher than Mary

[pic]

∴ No, Mary is not among the top 20% of students with the highest IQ scores. 25% of students obtain IQ scores higher than Mary.

(c) From the graph, 5 students have IQ scores 130 or above.

∴ The minimum score required to be admitted to the special programme is 130.

(d) From the graph, 10 students have IQ scores below 105.

∴ The lowest score of the students not taking the test again is 105.

|10. |(a) |Time less than (h) |Cumulative frequency |

| | |0.95 |0 |

| | |1.45 |15 |

| | |1.95 |37 |

| | |2.45 |64 |

| | |2.95 |100 |

| | |3.45 |128 |

| | |3.95 |140 |

(b)

[pic]

(c) From the graph, the number of students who spend less than 3.2 hours on watching TV every day is 114.

∴ The number of students who spend at least

3.2 hours on watching TV every day

[pic]

[pic]

11. (a)

[pic]

(b) Litres of petrol consumed[pic]L

Distance travelled per litre of petrol consumed

[pic]

From the graph, the number of cars which can travel a distance of less than 9.3 km is 154.

The number of cars which can travel a distance of

9.3 km or more

[pic]

[pic]

∴ 46 cars can travel a distance of 93 km or more on $200 of petrol.

12. [pic]

(a) From the graph, 50 tutors with fees lower than $150 per hour for centre A and 70 tutors with fees lower than $150 per hour for centre B.

∴ Percentage of tutors with fees lower than $150 per hour for centre A

[pic]

Percentage of tutors with fees lower than $150 per hour for centre B

[pic]

(b) From the graph, 30 tutors with fees lower than $140 per hour for centre A and 60 tutors with fees lower than $140 per hour for centre B.

∴ Percentage of junior tutors in centre A

[pic]

Percentage of junior tutors in centre B

[pic]

∴ Centre B has a higher percentage of junior tutors and the percentage of junior tutors is 30%.

(c) From the graph, 155 tutors with fees lower than $200 per hour for centre A and 140 tutors with fees lower than $200 per hour for centre B.

∴ Fraction of tutors with fees above $200 per hour for centre A

[pic]

Fraction of tutors with fees above $200 per hour for centre B

[pic]

∴ Centre B can offer the new course.

Exercise 7C (p. 7.42)

Level 1

1. (a) cumulative frequency polygon/curve

(b) histogram

(c) frequency polygon

2. Bar chart should be used because it can show the popularity of each favourite singer of S2 students.

3. Scatter diagram should be used because it can show the relationship between the examination result on each subject and the time spent on studying the corresponding subject.

4. Broken-line graph should be chosen because it can show the changes in average monthly temperature in 2008.

Level 2

5. (a) Stem-and-leaf diagram should be used because it can present a small amount of data exactly and the readers can read every datum from it.

| |(b) |Ages of 11 players in a football team |

| | |Stem (10) |Leaf (1) |

| | |1 |9 |

| | |2 |1 2 3 4 5 6 7 |

| | |3 |0 1 2 |

6. Angle of sector:

Hong Kong Island: 360° ( 30% = 108°

Kowloon: 360° ( 40% = 144°

The New Territories: 360° ( 20% = 72°

Islands: 360° ( 10% = 36°

[pic]

7.

[pic]

8. (a)

[pic]

(b) Number of customers participated in the survey

= 12 + 65 + 16 + 7

= 100

Angle of sector:

Excellent:[pic]

Satisfactory:[pic]

Unsatisfactory:[pic]

Poor:[pic]

[pic]

Exercise 7D (p. 7.48)

Level 1

1. (a) Figure (a) gives an impression that the company profit grew very fast.

(b) Figure (b) presents the profit growth of the company appropriately because the vertical axis starts from zero.

2. (a) Monthly sales of brand A : monthly sales of brand B

[pic]

[pic]

(b) No, the ratio of their areas is not the same as that found in (a).

(c) Yes, this statistical diagram misleads readers because it gives an impression that the monthly sales of brand A milk powder is much higher than that of brand B.

3. (a) Sales of brand A : sales of brand B : sales of brand C

[pic]

[pic]

(b) No, the ratio of the areas of the bottles drawn is not equal to that obtained in (a).

(c) No. Since the ratio of the sales of brands A, B and C is 4 : 3 : 2, there is no big lead for the sales of brand A.

4. (a) The best mark[pic], the worst mark[pic]

(b) The required percentage[pic]

(c) No. Since the last 10 English dictations marks for David all lie within 94 and 98 marks. Therefore, I do not agree with Edward’s claim that David’s performance in English dictation was unstable.

Level 2

5. It cannot be determined. Since the pie charts only give the angle of sector of each item, but not the total expenditure of Mr Wong and Mr Lee, we do not know their monthly savings, and hence cannot do the comparison.

6. (a) ∵ Harvest in 2005: 30 tons

Harvest in 2007: 40 tons

Harvest in 2008: 60 tons

∴ The farmer’s harvest in 2008 is 1.5 times that of 2007 and 2 times that of 2005.

∴ His son’s conclusion is not correct.

(b) [pic]

7. (a) Percentage increase in number of customers from 2004 to 2008 in the Causeway Bay branch

[pic]

Percentage increase in number of customers from 2004 to 2008 in the Tsim Sha Tsui branch

[pic]

(b) Yes, the two diagrams mislead readers because the vertical axes do not start from zero.

8. No, although the percentage increase in sales of brand D cooking oil in 2008 is the highest, its sales is the lowest among the 4 different brands.

9. It cannot be determined because we do not know the component of others on the pie chart.

Revision Exercise 7 (p. 7.55)

Level 1

1. (a) The class interval 23.8(C – 24.2(C has the highest frequency.

(b) (i) Number of office buildings having an average air temperature at or above 25.25(C

[pic]

[pic]

(ii) Number of office buildings having an average air temperature between 23.25(C – 25.25(C

[pic]

[pic]

|2. |Time (min) |Class mark (min) |Frequency |

| |30 – 59 |44.5 |0 |

| |60 – 89 |74.5 |4 |

| |90 – 119 |104.5 |5 |

| |120 – 149 |134.5 |10 |

| |150 – 179 |164.5 |12 |

| |180 – 209 |194.5 |6 |

| |210 – 239 |224.5 |3 |

| |240 – 269 |254.5 |0 |

[pic]

|3. |Height (cm) |150– |

|(a) | |154 |

| |19.5 |0 |

| |39.5 |5 |

| |59.5 |12 |

| |79.5 |23 |

| |99.5 |41 |

| |119.5 |51 |

| |139.5 |60 |

[pic]

6. [pic]

The cumulative frequency that corresponds to the lower quartile

= 25% ( 40

= 10

From the graph, the height corresponds to a cumulative frequency of 10 is 149.5 cm.

∴ Lower quartile[pic]

The cumulative frequency that corresponds to the median

= 50% ( 40

= 20

From the graph, the height corresponds to a cumulative frequency of 20 is 155.5 cm.

∴ Median[pic]

The cumulative frequency that corresponds to the upper quartile

= 75% ( 40

= 30

From the graph, the height corresponds to a cumulative frequency of 30 is 160.5 cm.

∴ Upper quartile[pic]

7. [pic]

(a) The cumulative frequency that corresponds to the 20th percentile

= 20% ( 100

= 20

From the graph, the age that corresponds to a cumulative frequency of 20 is 64.5.

∴ The 20th percentile[pic]

The cumulative frequency that corresponds to the 30th percentile

= 30% ( 100

= 30

From the graph, the age that corresponds to a cumulative frequency of 30 is 67.

∴ The 30th percentile[pic]

(b) From the graph, 68 patients have ages at or above 74.5.

∴ Percentage of patients who will pay the lower fee

[pic]

8. (a) frequency polygon/curve (or any other reasonable answers). It is used to show the changes in frequencies of the class interval.

(b) broken-line graph (or any other reasonable answers). It is used to show the change in frequencies of data over a period of time and the trend of data.

(c) frequency polygon/curve (or any other reasonable answers). It is used to show the changes in frequencies of the class interval.

(d) scatter diagram (or any other reasonable answers). It is used to show the relationship between two quantities.

(e) pie chart (or any other reasonable answers). It is used to show the percentage of each item.

9. (a) Sales in 2007[pic]

Sales in 2008[pic]

(b) Percentage increase of sales in 2008

[pic]

[pic]

(c) No. The diagram gives readers an impression that the sales in 2008 is much higher than that of 2007.

Level 2

|10. (a) |Pulse rate less than (beats |Cumulative frequency |

| |per minute) | |

| |60.5 |0 |

| |65.5 |5 |

| |70.5 |27 |

| |75.5 |58 |

| |80.5 |81 |

| |85.5 |96 |

| |90.5 |100 |

(b)

[pic]

(c) From the graph,

the number of patients whose pulse rates are 82 beats per minute or above

[pic]

[pic]

11. [pic]

(a) Number of students who need to take remedial classes

[pic]

From the graph, 6 students take 65 minutes or more to finish the test.

∴ The slowest time among students who do not have to take remedial classes is 65 min.

(b) From the graph, the cumulative frequency that corresponds to 42 min = 8

∴ Percentage of students who take less than 42 minutes to finish the test

[pic]

∴ No, Jenny is not among the fastest 10% of students who finish the test.[pic]of students take less than 42 minutes to finish the test.

(c) From the graph, the cumulative frequency that corresponds to 60 min = 45

∴ Fraction of students who can finish the test within 1 hour

[pic]

∴ Yes, Paul is correct.

|12. (a) |Marks |Class |Class |Frequency |

| | |boundaries |mark | |

| |30 – 39 |29.5 – 39.5 |34.5 |4 |

| |40 – 49 |39.5 – 49.5 |44.5 |6 |

| |50 – 59 |49.5 – 59.5 |54.5 |7 |

| |60 – 69 |59.5 – 69.5 |64.5 |10 |

| |70 – 79 |69.5 – 79.5 |74.5 |6 |

| |80 – 89 |79.5 – 89.5 |84.5 |5 |

| |90 – 99 |89.5 – 99.5 |94.5 |2 |

(b)

[pic]

(c)

[pic]

13. (a) Total number of books = 896 + 1190 + 1722 + 1232

= 5040

Angle of sector:

Pure Science:[pic]

Social Science:[pic]

Languages:[pic]

Fiction:[pic]

[pic]

(b) (i) Total number of books

= 1552 + 301 + 722 + 1360

= 3935

Angle of sector:

Pure Science:[pic]

Social Science:[pic]

Languages:[pic]

Fiction:[pic]

[pic]

[pic]

(ii)

[pic]

14. (a) Yes. The broken-line graph gives readers an impression that the magazine has a remarkable increase in sales in the first 6 months of 2008.

(b) [pic]

15. (a) No, we cannot find the prices of the shampoos from the above graph.

(b) No, since from (a), we do not know the actual prices of the 5 brands of shampoo.

|16. (a) |Weight less than (g) |Cumulative frequency |

| |199.5 |0 |

| |219.5 |4 |

| |239.5 |13 |

| |259.5 |25 |

| |279.5 |38 |

| |299.5 |45 |

| |319.5 |50 |

| (b) |Weight (g) |Frequency |

| |200 – 219 |4 |

| |220 – 239 |9 |

| |240 – 259 |12 |

| |260 – 279 |13 |

| |280 – 299 |7 |

| |300 – 319 |5 |

17. (a) From the frequency polygon of group A students, the class boundaries of the last class interval are 69.5 s and 71.5 s. Therefore, there are no students taking 71.5 s or longer to run 400 m in group A.

(b) Yes, since the frequency polygon of the time taken by group A students lies to the left of that of group B students, group A performs better than group B in general.

(c) Number of students from group A who can qualify

[pic]

Number of students from group B who can qualify

[pic]

(d) Number of students from group A who take less than 67.5 s to finish 400 m

[pic]

Number of students from group B who take less than 67.5 s to finish 400 m

[pic]

Number of students in the combined team

[pic]

-----------------------

Average time of 140 S2 students spend

on watching TV every day

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download