Chapter 6Analysis of Statistical Graphs 6.1
Chapter 6Analysis of Statistical Graphs
Warm-up Exercise1.The following frequency distribution table shows the number of hours spent on watching television each day among a group of students.
Number of hours / 0 / 1 / 2 / 3 / 4 / 5 / 6 / 7Frequency / 4 / 8 / 10 / 16 / 14 / 5 / 2 / 1
(a)Find the number of students in this group.
(b)How many students have watched television for 4 hours or more each day?
2.The following figure shows the favourite colours of mobile phones among a group of people.
(a)Find the number of people in this group.
(b)Which two colours of mobile phones do least people like?
3.The following table shows the number of brothers and sisters among 30 students.
1 / 2 / 4 / 0 / 3 / 1 / 2 / 0 / 0 / 12 / 2 / 3 / 1 / 1 / 4 / 0 / 1 / 0 / 5
4 / 2 / 2 / 3 / 0 / 2 / 1 / 1 / 1 / 0
(a)Organize the above data by using the frequency distribution table below.
Number of brothers and sisters / Tally / FrequencyTotal
(b)How many students in this group do not have any brothers or sisters?
Build-up Exercise[ This part provides two extra sets of questions for each exercise in the textbook, namely Elementary Setand Advanced Set. You may choose to complete any ONE set according to your need. ]
Exercise 6A
Elementary Set
Level 1
1.Write down the following terms in the appropriate brackets.
[A copy of the figure is provided in the Appendix.]
Upper classLower classUpper classLower classClass widthClass mark
limitlimitboundaryboundary
2.The following frequency distribution table shows the heights of students in S2A.
Height (cm) / Frequency120 - 124 / 3
125- 129 / 5
130-134 / 11
135-139 / 14
140-144 / 7
145-149 / 4
(a)(i)Find the upper class boundary of the fourth class.
(ii)Find the lower class boundary of the fourth class.
(iii)Find the class mark of the fourth class.
(b)Find the number of students with heights between 129.5cm and 144.5cm.
3.The following frequency distribution table shows the weights of MP3 players in an audio video store.
Weight (g) / Frequency30 - 49 / 2
50 -69 / 6
70-89 / 9
90-109 / 12
110-129 / 18
130-149 / 3
150 - 169 / 1
(a) (i)Find the upper class boundary of the fourth class.
(ii)Find the lower class boundary of the fourth class.
(iii)Find the class mark of the fourth class.
(b)Find the number of MP3 players with weights less than 109.5g.
4.The following frequency distribution table shows the weights of 50 bags of vegetables.
Weight (kg) / 0.2-0.5 / 0.6-0.9 / 1.0- 1.3 / 1.4- 1.7 / 1.8 - 2.1 / 2.2 - 2.5Frequency / 4 / 7 / 14 / 17 / 5 / 3
(a)What is the class width?
(b)Find the percentage of vegetables with weights less than 1.75kg per bag.
5.The following frequency distribution table shows the weights of 50 S1 boys.
Weight (kg) / 30 - 35 / 36 - 41 / 42 - 47 / 48 - 53 / 54 - 59 / 60 - 65Frequency / 3 / 11 / x / 10 / 1 / 2
(a)What is the value of x?
(b)Which class interval has the greatest number of boys?
(c)If a weight between 41.5kg and 53.5kg is regarded as a standard weight, find the percentage of boys with standard weight.
Level 2
6.The following shows the respective time taken by 20 athletes to finish 100m, correct to the nearest 0.1 second.
13.1 / 14.2 / 13.1 / 15.2 / 13.4 / 14.0 / 14.8 / 13.2 / 14.0 / 13.513.0 / 13.9 / 13.4 / 14.3 / 14.8 / 15.0 / 14.2 / 14.7 / 13.4 / 13.0
According to the above data, complete the table below.
Time(second) / Tally / Frequency13.0 - 13.4
13.5 - 13.9
14.0 - 14.4
14.5 - 14.9
15.0 - 15.4
Total
7.The following shows the number of turns made by a group of students skipping rope in one minute. Construct a frequency distribution table by using 40-44 as the first class interval.
42 / 45 / 47 / 53 / 40 / 49 / 68 / 72 / 65 / 5968 / 74 / 48 / 47 / 48 / 52 / 56 / 63 / 65 / 71
64 / 59 / 60 / 60 / 70 / 43 / 51 / 55 / 55 / 65
Advanced Set
Level 1
1.The following frequency distribution table shows the respective time taken by 30athletes to finish 400m, correct to the nearest 0.1 second.
Time(second) / Frequency54.0 - 57.4 / 4
57.5 - 60.9 / 8
61.0 - 64.4 / 7
64.5 - 67.9 / 5
68.0 - 71.4 / 6
(a)What are the upper and lower class limits of the second class?
(b)What is the class mark of the fourth class?
2.(a)The following table shows the time spent on watching television each day among 40students.Complete the table.
Time (minute) / Class boundaries (minute) / Class mark (minute) / Frequency1 - 30 / 3
31 - 60 / 6
61 - 90 / 12
91 - 120
121 - 150 / 6
151 - 180 / 7
Total / 40
(b)What is the class width?
(c)Find the percentage of students who have watched television for less than 60.5minutes each day.
3.(a)The following table shows the weights of 40 S1 girls.Complete the table.
Weight (kg) / Class boundaries (kg) / Class mark (kg) / Frequency26 - 30 / 2
31 - 35 / 9
36 - 40 / 13
41 - 45 / 8
46 - 50 / 5
51 - 55
Total / 40
(b)Which class interval has the greatest number of girls?
(c)If girls with weights less than 35.5 kg are regarded as underweight, find the percentage of girls who are underweight.
Level 2
4.The following shows the average lapse time of sports cars in a car race, correct to the nearest second.
234 / 221 / 242 / 254 / 243 / 238 / 242 / 239227 / 229 / 263 / 236 / 234 / 235 / 240 / 239
241 / 256 / 250 / 229 / 230 / 239 / 264 / 248
252 / 247 / 265 / 246 / 232 / 234 / 257 / 248
(a)According to the above data, complete the table below.
Time (second) / Class boundaries(second) / Class mark
(second) / Tally / Frequency
220 - 229
Total
(b)What is the class width?
(c)Find the percentage of sports cars with average lapse time less than 239.5seconds.
5.The following shows the results of 40students in S2A in an English Language test.
40 / 40 / 45 / 49 / 52 / 53 / 54 / 54 / 58 / 5860 / 60 / 61 / 62 / 62 / 64 / 65 / 65 / 69 / 69
70 / 71 / 73 / 74 / 75 / 75 / 76 / 77 / 78 / 79
79 / 79 / 81 / 82 / 84 / 88 / 88 / 90 / 95 / 98
(a)According to the above data, completethe tables below.
(i) / Score / Tally / Frequency40 - 44
45 - 49
50 - 54
55 - 59
60 - 64
65 - 69
70 - 74
75 - 79
80 - 84
85 - 89
90 - 94
95 - 99
Total / 40
(ii) / Score / Tally / Frequency
40 - 49
50 - 59
60 - 69
70 - 79
80 - 89
90 - 99
Total / 40
(b)Which of the above two frequency distribution tables can better reveal the tendency of the data?
6.The following shows the heights of 40students in S2B, correct to the nearest cm.
150 / 152 / 153 / 153 / 154 / 154 / 155 / 156 / 156 / 158159 / 159 / 160 / 161 / 161 / 162 / 163 / 164 / 164 / 164
165 / 165 / 165 / 166 / 166 / 167 / 168 / 168 / 168 / 169
170 / 171 / 172 / 174 / 174 / 175 / 176 / 177 / 177 / 179
(a)Which class width, 2cm, 5cm or 10cm, is most suitable for the above data?
(b)Find the class interval of each of the classes by using the class width in (a).
(c)Construct a frequency distribution table according to the class intervals in (b).
7.The following shows the weights of 30boxes of nuts, correct to the nearest 0.1g.
150.3 / 149.8 / 150.2 / 148.2 / 151.4 / 151.2 / 150.1 / 148.9 / 148.7 / 150.8149.6 / 149.5 / 148.6 / 150.1 / 150.2 / 150.3 / 151.2 / 150.2 / 149.9 / 150.0
148.0 / 148.3 / 150.4 / 150.1 / 148.7 / 149.0 / 150.6 / 151.1 / 149.4 / 149.9
(a)Which class width, 0.2g, 0.5g or 1g, is most suitable for the above data?
(b)According to the class width in (a), construct a frequency distribution table and list the class boundaries and class mark of each of the classes.
8.The following stem-and-leaf diagram shows the speeds of cars detected by the police on a road on a certain day.
(a)By using 70km/h-74km/h as the first class interval, construct a frequency distribution table and list the class boundaries and class mark of each of the classes.
(b)Which class interval has the highest frequency?
(c)If the speed of any car on the road exceeds 104.5km/h, the driver will be fined. How many drivers on the road that day will be fined? What percentage of drivers are fined?
Exercise 6B
Elementary Set
Level 1
1.Determine whether each of the following statements is correct. If yes, put a ‘’ in the box; otherwise put a ‘’.
(a)In a histogram, there are gaps between two rectangular bars.□
(b)In a histogram, the area of a bar is proportional to its frequency.□
(c)In a bar chart, there are gaps between two bars.□
(d)Discrete data can only be presented by histograms.□
(e)There must be a title in a histogram.□
2.Thehistogram shows the monthly traffic expenses of S1 students.
(a)How many students are there in the class with the greatest number of students?
(b)How many students are there in the class with the smallest number of students?
(c)How many students are there with traffic expenses between $199.5 and $399.5?
3.Thehistogram shows the ages of employees in a company. It is given that the first class interval is 21 - 30.
(a)Find the class boundaries and class interval of the third class.
(b)Which class interval has the greatest number of employees? How many employees are there in this class interval?
4.Thehistogram shows the scoresof S2A students in an English Language test.
(a)How many students are there in S2A?
(b)Find the class boundaries of each of the classes.
(c)How many students have obtained scores 60.5 or above?
Level 2
5.(a)The following table shows the monthly incomes of a group of readers of a magazine. Complete the table.
Monthly income ($) / Class boundaries ($) / Class mark ($) / Frequency1 - 10000 / 0.5 - 10000.5 / 5000.5 / 30
10001 - 20000 / 42
20001 - 30000 / 27
30001 - 40000 / 15
40001 - 50000 / 6
Total
(b)Construct a histogram according to the above table.
6.(a)The following frequency distribution table shows the weights of 200apples.
Weight (g) / Frequency180 - 189 / 27
190 - 199 / 52
200 - 209 / 47
210 - 219 / 42
220 - 229 / 32
According to the above information, complete the table below.
Weight (g) / Class boundaries (g) / Class mark (g) / FrequencyTotal
(b)Construct a histogram according to the above table.
Advanced Set
Level 1
1.Thehistogram shows the time spent by S1 students on sports each day.
(a)How many students are there in the class with the greatest number of students?
(b)How many students are there in the class with the smallest number of students?
(c)How many students have spent 29.5minutes to 59.5minutes on sports each day?
2.Thehistogram shows the weights of schoolbags among S2A students.
(a)How many students are there in S2A?
(b)Find the class boundaries of each of the classes.
(c)How many students are there with schoolbags weighing more than 5.5kg?
3.Thehistogram shows the results of 200candidates in a public examination. It is given that the first class interval is 30-39.
(a)Which class interval has the smallest number of candidates? How many candidates are there in this class interval?
(b)If candidates with scores 79.5 or above will get grade A, how many candidates will get grade A in the examination?
(c)If candidates with scores below 49.5 will fail in the examination, what percentage of the candidates will fail in the examination?
Level 2
4.(a)The following table shows the heights of 100students. Complete the table.
Height (cm) / Class boundaries (cm) / Class mark (cm) / Frequency150 - 154 / 4
155 - 159 / 18
30
19
2
Total / 100
(b)Construct a histogram according to the above table.
5.(a)The following table shows the age distribution of members in a fitness centre. Complete the table.
Age / Class boundaries / Class mark / Frequency15 - 19 / 14.5 - 19.5 / 17 / 12
20 - 24 / 30
25 - 29 / 24
30 - 34 / 18
35 - 39 / 6
Total
(b)Construct a histogram according to the above table.
6.The following frequency distribution table shows the weights of 200oranges.
Weight (g) / Frequency170 - 179 / 20
180 - 189 / 65
190 - 199 / 35
200 - 209 / 44
210 - 219 / 36
(a)According to the above information, complete the table below.
Weight (g) / Class boundaries (g) / Class mark (g) / FrequencyTotal
(b)Construct a histogram according to the above table.
(c)If only oranges with weights of 199.5g or above are acceptable, find the percentage of oranges with unacceptable weights.
Exercise 6C
Elementary Set
Level 1
1.The following frequency polygon shows the monthly pocket money of 40 S2 students.
According to the above figure, complete the table below.
Pocket money($) / Class mark ($) / Frequency400 - 599
600 - 799
2.(a)The following table shows the monthly fees for mobile phones of 200 people. Complete thetable.
Monthly fee ($) / Class boundaries ($) / Class mark ($) / Frequency21 - 50 / 20.5 - 50.5 / 35.5 / 21
51 - 80 / 64
81 - 110 / 58
111 - 140 / 42
141 - 170 / 15
Total / 200
(b)According to the above table, construct a frequency polygon in the figure below.
[A copy of the figure is provided in the Appendix.]
3.(a)The following table shows the long jump results of 100 athletes. Complete thetable.
Distance (m) / Class boundaries (m) / Class mark (m) / Frequency3.01 - 3.20 / 5
3.21 - 3.40 / 12
3.41 - 3.60 / 23
3.61 - 3.80
3.81 - 4.00 / 18
4.01 - 4.20 / 15
4.21 - 4.40 / 2
Total / 100
(b)According to the above table, construct afrequency polygon in the figure below.
[A copy of the figure is provided in the Appendix.]
4.The following frequency polygon shows the respective time taken by 60 people to finish 800m.
(a)According to the above frequency polygon, complete the table below.
Time (second) / Class mark (second) / Frequency115 - 119 / 117
120 - 124 / 122
(b)Which class interval has the greatest number of people? How many people are there in this class interval?
5.The following frequency polygon shows the number of hours spent on watching football matches each week among 100people.
(a)According to the above frequency polygon, complete the table below.
Number of hours / Class mark / Frequency3 - 5
(b)How many people have watched football matches for 11.5hours or more each week? What is the percentage of people do they cover?
Level 2
6.The following frequency curve shows the ages of customers buying albums of singers A and B in an audio store yesterday.
According to the above figure,
(a)which singer’s albums attract customers younger than 18?
(b)which singer has younger fans?
7.The following frequency polygon shows the scores of S2A and S2B students in a Mathematics examination.
(a)Which class has students with scores below 20.5?
(b)If students with scores 80.5 or above will be awarded, how many students will be awarded in each class?
(c)Which class has a better performance?
(d)Which class needs to make more effort on mathematics?
Advanced Set
Level 1
1.(a)The following table shows the time of using mobile phone each month among 200people. Complete the table.
Time (minute) / Class boundaries (minute) / Class mark (minute) / Frequency51 - 100 / 50.5 - 100.5 / 75.5 / 10
101 - 150 / 35
151 - 200 / 50
201 - 250 / 43
251 - 300 / 24
301 - 350 / 23
351 - 400 / 15
Total / 200
(b)According to the above table, construct a frequency polygon in the figure below.
[A copy of the figure is provided in the Appendix.]
2.(a)The following table shows the time spent by 40 people at a bank counter. Complete the table.
Time (minute) / Class boundaries (minute) / Class mark (minute) / Frequency2 - 5 / 1.5 - 5.5 / 3.5 / 5
6 - 9 / 5.5 - 9.5 / 13
10 - 13 / 18
14 - 17 / 15.5 / 4
(b)According to the above table, construct a frequency polygon in the figure below.
[A copy of the figure is provided in the Appendix.]
3.The following frequency polygon shows the number of hours spent on reading each week among 100people.
(a)According to the above frequency polygon, complete the table below.
Number of hours / Class mark / Frequency4 - 8
(b)How many people are spending23.5 hours or more on reading each week? What percentage of people do they cover?
Level 2
4.The following frequency polygon shows the results of two classes of students in a Chinese Language test.
(a)Find the respective number of students in the two classes.
(b)Which class has better results in general?
(c)If there is another Chinese Language test, which class is more likely to have better results? Why?
5.Thefrequency polygon shows the heights of the players in basketball teams A and B.
(a)Find the respective number of players in the two teams.
(b)Which team has taller players in general?
(c)Which team do you think is more likely to win? Why?
6.The following frequency distribution table shows the lifetime of brands A and B batteries.
Lifetime (hour) / 11 - 12 / 13 - 14 / 15 - 16 / 17 - 18 / 19 - 20Brand A / 16 / 28 / 35 / 16 / 5
Brand B / 20 / 32 / 27 / 14 / 7
(a)Construct a frequency polygon to represent the lifetime of brands A and B batteries.
(b)Which batteries, brands A or B, have longer lifetime in general?
(c)If a Brand A battery is selected, what is its most possible lifetime?
7.The following is the average monthly service time of 50 volunteers in a social service centre, correct to the nearest 0.1hour. Using 1 hour - 5 hours as the first class interval, draw a frequency polygon to present the data.
4.2 / 27.5 / 14.1 / 2.3 / 25.2 / 5.6 / 8.4 / 26.4 / 13.6 / 33.033.4 / 37.5 / 19.2 / 7.4 / 12.3 / 32.8 / 26.5 / 4.2 / 6.8 / 15.7
20.4 / 5.9 / 11.9 / 27.3 / 21.9 / 22.4 / 11.0 / 4.4 / 24.8 / 37.9
8.1 / 15.9 / 28.4 / 35.2 / 2.6 / 22.5 / 14.4 / 17.5 / 13.9 / 31.0
36.7 / 6.0 / 2.4 / 28.7 / 38.5 / 25.6 / 27.3 / 37.3 / 21.4 / 25.6
Exercise 6D
Elementary Set
Level 1
1.The following table shows the weights of 100 S2 students. Construct a cumulative frequency table to present the data.
Weight (kg) / Frequency40 - 44 / 11
45 - 49 / 20
50 - 54 / 36
55 - 59 / 24
60 - 64 / 9
2.The following table shows the weights of schoolbags of S2 students in a school. Construct a cumulative frequency table to present the data.
Weight of schoolbag (kg) / Frequency3.0 - 3.1 / 12
3.2 - 3.3 / 40
3.4 - 3.5 / 48
3.6 - 3.7 / 54
3.8 - 3.9 / 30
4.0 - 4.1 / 14
4.2 - 4.3 / 2
3.The following cumulative frequency polygon shows the scores of 100 students in a common knowledge quiz.
(a)If the top 40% students will receivesouvenirs, find the score required for receiving a souvenir.
(b)If a student with a score of 80 or above will further receive a certificate, what percentage of students will receive a certificate?
4.Thecumulative frequency curve shows the time taken by a group of students to do 30sit-ups.
(a)How many students are there in this class?
(b)How many students can do 30 sit-ups within32 seconds?
(c)If students who take 40 seconds or more to finish 30 sit-ups need to do another 30 sit-ups, how many students need to do additional 30sit-ups?
Level 2
5.The following table shows the results of S2A students in a Chinese Language examination.
Score / Frequency21 - 30 / 1
31 - 40 / 5
41 - 50 / 10
51 - 60 / 11
61 - 70 / 7
71 - 80 / 4
81 - 90 / 2
91 - 100 / 0
(a)Construct a cumulative frequency table.
(b)Construct a cumulative frequency polygon.
[For the horizontal axis, 5units10marks; for the vertical axis, 1unit1student.]
6.The following table shows the parking time of cars in a car park.
Parking time (hour) / Frequency1 - 3 / 28
4 - 6 / 24
7 - 9 / 23
10 - 12 / 16
13 - 15 / 5
16 - 18 / 2
19 - 21 / 1
22 - 24 / 1
(a)Construct a cumulative frequency table.
(b)Construct a cumulative frequency polygon.
[For the horizontal axis, 6units3hours; for the vertical axis, 1unit2cars.]
(c)Find the number of cars which have parked for 15.5hours or above.
(d)Find the percentage of cars which have parked for less than 9.5hours.
(e)Suggest a method to encourage car owners to park their cars for a longer period of time.
Advanced Set
Level 1
1.The following table shows the satisfactory level (with a full score of 100) of 200citizens towards their living in a city. Construct a cumulative frequency table to present the data.
Satisfactory level / Frequency21 - 30 / 1
31 - 40 / 3
41 - 50 / 8
51 - 60 / 22
61 - 70 / 73
71 - 80 / 47
81 - 90 / 25
91 - 100 / 21
2.Thecumulative frequency curve shows the time taken by a group of students to finish 20 push-ups.
(a)How many students are there in this group?
(b)How many students can finish 20push-ups within 20 seconds?
(c)If students who take 24 seconds or more to finish 20 push-ups need to attend a physical training course, how many students need to attend the course?
3.Thecumulative frequency polygon shows the average sleeping time of a group of students.
(a)How many students are there in this group?
(b)How many students are sleeping less than 7.5hours on average? What percentage of students do they cover?
(c)For the 10 students with the longest average sleeping time, what is the shortest average sleeping time among them?
Level 2
4.The following table shows the time of a group of people staying in a library one day.
Duration of stay (minute) / Frequency0 - 29 / 10
30 - 59 / 20
60 - 89 / 25
90 - 119 / 35
120 - 149 / 50
150 - 179 / 30
180 - 209 / 5
210 - 239 / 5
(a)Construct a cumulative frequency table.
(b)Construct a cumulative frequency polygon.
[For the horizontal axis, 5units30minutes; for the vertical axis, 1unit5people.]
5.The following table shows the distribution of the journey time of each bus trip on route A one day.
Time (minute) / Frequency41 - 45 / 4
46 - 50 / 12
51 - 55 / 33
56 - 60 / 24
61 - 65 / 15
66 - 70 / 10
71 - 75 / 1
76 - 80 / 1
(a)Construct a cumulative frequency table.
(b)Construct a cumulative frequency polygon.
[For the horizontal axis, 5units5minutes; for the vertical axis, 1unit2bus trips.]
(c)Given that the journey time of a bus trip during peak hours is at least 65.5minutes, how many bus trips are there during peak hours?
(d)Find the percentage of bus trips with journey time less than 50.5minutes.
(e)For what reason do you think will the journey time of a bus trip be less than 50.5minutes?
6.The following is the respective time spent on using ICQ one day among S2C students, correct to the nearest minute.
71 / 100 / 116 / 23 / 185 / 65 / 94 / 12 / 135 / 13989 / 37 / 10 / 202 / 74 / 209 / 163 / 28 / 115 / 55
41 / 125 / 235 / 195 / 119 / 94 / 169 / 56 / 54 / 49
139 / 134 / 21 / 174 / 221 / 164 / 29 / 210 / 121 / 145
(a)Construct a frequency distribution table by using 1 minute - 30 minutes as the first class interval.
(b)Construct a cumulative frequency table.
(c)Construct a cumulative frequency polygon.
[For the horizontal axis, 5units30minutes; for the vertical axis, 1unit1 student.]
(d)Hence
(i)findthe number of students spending 60.5 minutes or above on using ICQ.
(ii)find the percentage of students spending 120.5 minutes to 180.5 minutes on using ICQ.