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Chapter 1 Exercise 1.1
Q. 1. Tanya collected the data and she will use it in her presentation, so it is primary data.
Q. 2. (i) Observation
(ii) Questionnaire
(iii) Carrying out experiments
Q. 3. Conor did not write the Guinness Book of Records, so he did not collect the data that he will use.
Q. 4. (i) CSO (Central Statistics Office)
(ii) ESRI
Q. 5. (i) A good sample can be chosen
(ii) Quick feedback
Q. 6. You cannot choose the sample, and it can be expensive.
Q. 7. The population is the entire group that is being studied.
A sample is a group that is selected from the population.
Q. 8. A census
Q. 12. (i) Use clear and simple language.
(ii) Accommodate all possible answers.
(iii) Be clear where answers should be recorded.
(iv) Make sure the questions are relevant to the survey.
(v) Open with a simple question to encourage people to complete the survey.
(vi) Be as brief as possible.
Q. 13. (i) We don’t know what age young, middle-aged or old is (the question is not clear).
(ii) How old are you?
0–18 19–45 46 +
Q. 14. (i) It does not account for every possible answer.
(ii) How often do you watch a football game?
Never Once a week Twice a week or more
Q. 15. (i) It is unlikely anybody knows the answer.
(ii) Many people will not disclose this information. Also, somebody earning between €40,000 and €50,000 does not have a checkbox to tick.
Q. 16. The question is not clear because people who live on farms also live in the country.
Q. 17. Very few subjects will be familiar with Article 4 of the constitution.
2
Q. 18. Gender: Male Female
Age: 0–18 19–30 31–50
50–65 66+
How many hours of television do you watch every day?
0–1 1–2 2–3 3+
Q. 19. (i) The sample includes only people who go to the theatre. (ii) People who did not attend are not surveyed. (iii) The sample is not a random sample. (iv) Sometimes people will not disclose how much they spend.
Q. 20. The sample size is too small. The sample is not a random sample.
Q. 21. Only First Year students are surveyed and the population of interest is the whole school population. Bob should have taken a simple random sample of the whole school population. Playstation games played by Fifth Years are possibly quite different to the games First Years would play. Therefore, the sample is biased in favour of First Years.
Q. 22. People in the neighbourhood who drive cars may not be in favour of a pedestrian crossing, as it could load to delays. In most neighbourhoods, the number of people who drive cars would far outnumber pedestrians. So car owners in the sample would outnumber pedestrians. In this particular situation, we need to bias the sample in favour of pedestrians; otherwise there would be no chance of getting the crossing.
Exercise 1.2
Q. 1. (i) Age 12 13 14 15
Tally ||||||||||||||||||||||||||||||||||| ||||||||||||||||||||||||||||||||||||||||||||||||||| ||||||||| ||||||||||||||||||||||||||||||||| |||||||| ||||||
|||||||| |||| |||| ||||| ||||||||||||||||||||||||||||||||||
Frequency 9 7 11 3
(ii) 9 + 7 + 11 +3 = 30
Q. 2. (i) Score 1 2 3 4 5 6
Tally |||||||||||||||||||||||||||||||||||||||||||||||||| |||||||||| |||| |||||||||||||||||||||||||| |||||||||| |||||||||||||||||||||||||||||||||||||||||||||||||| |||||||||| |||||||||||||||||||||||||||||||||||||||| ||||||||| |||| |||||| || |||||||||||||||||||||||||| | |||| ||||||||||||||||||||||||||||||||||||||||||||||||| |||||||||| |||||||||||||||||||||||||||||||||||||||| |||||||||| |||||| |||||||||||||||||||||||||||||||||||||||| ||||||||| |||| |||||||||||||||||||||||||||||||||||| ||||||||||
Frequency 10 10 7 5 8 10
(ii) 6
(iii) 10
(iv) 5 ___ 50 × 100 = 10%
Q. 3. (i) Mode Walk Bus Car Rail
Frequency 9 5 4 2
(ii) Walk(iii) Rail
3
Q. 4. Mark 4 5 6 7 8 9 10
Frequency 2 1 4 5 5 9 4
(i) 2 + 1 + 4 + 5 + 5 + 9 + 4 = 30
(ii) 4 ___ 30 = 2 ___ 15
Q. 5. (i) Number 1 2 3 4 5 6
Frequency 6 8 8 4 2 2
(ii) 4 + 2 + 2 = 8(iii) 6 + 8 + 8 = 22
Total = 30
� 22 ___ 30
× 100 ____ 1 = 7313%
Q. 6. (i) Number 0 1 2 3 4
Frequency 7 9 11 3 5
(ii) 7 + 9 + 11 + 3 + 5 = 35(iii) 7
(iv) 7 + 11 + 5 = 23(v) 7
Q. 7. (i) Result 3 H 2 H 1 H 0 H
Tally |||||| ||||||||||||||||||||||||||||||||||||||||| |||| ||||| || ||||||||||||||||||||||||||||||||| ||||||||||||||||||||||||||||||||||||||||| |||||||| ||||
Frequency 3 11 9 2
(ii) 9 ___ 25 × 100 = 36%
Exercise 1.3
Q. 1.
X
XXX
XXX
X
X
X
Movie CornerCinema Station
DVD Rental
Planet DVD
Q. 2.
XX
XXX
XX
XX
XXXX
200820072006
4
Q. 3.
XX X
X
XX
XXXX
XXX
AprMarFebJan
Q. 4. (i) Tom
(ii) John
(iii) 4 + 5 + 4 + 3 = 16
(iv) 4 ___ 16
× 100 ____ 1
= 25%
Exercise 1.4
Q. 1. (i) 876543210
Blue Red Green Yellow Black Orange
Favourite colours
Nu
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(ii) Red
(iii) Orange
(iv) 7 + 8 + 4 + 4 + 3 + 2 = 28
(v) 7 ___ 28 × 100 ____ 1
= 25%
Q. 2. (i) Evelyn
(ii) Derek
(iii) 4 + 2 + 4 + 0 + 7 = 17
(iv) Alan and Carol
(v) Betty and Evelyn scored 2 + 7 = 9 goals. They scored more than half the goals, as half the total goals is 8.5.
Q. 3. (i) 876543210
Paula Seán James Tanya RosieCandidates
Class elections
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(ii) Paula and Tanya
5
(iii) Total = 8 + 4 + 3 + 7 + 5 = 27
James = 3 ___ 27
= 1 __ 9
Q. 4. (i) 109876543210
7 8 9 10 11Age
Book club
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(ii) 10
(iii) 10 ___ 30 = 1 __ 3
(iv) 2 ___ 30 × 100 ____ 1 = 6.67%
Q. 5. (i) 40
(ii) 50 + 40 + 20 + 25 + 50 + 50 + 60 = 295
(iii) 60 ____ 295 × 100 ____ 1 = 20.34%
(iv) Most people don’t work on Sundays, so they have time to read the paper.
Q. 6. (i) 876543210
Belgium Denmark Ireland Holland AustriaCountry
Country area
Are
a (
×10,000
km2 )
(ii) Denmark = 4 × 10,000 km2 = 40,000 km2
(iii) Austria = 80,000 km2 = Area of Holland and Denmark.
(iv) Belgium = 30,000 km2
Ireland = 70,000 km2
� Percentage = 30,000 km2
___________ 70,000 km2 × 100 ____ 1 = 42.86%
= 43% (to the nearest whole number)
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Q. 7. (i) 876543210
Soccer Rugby Football Hurling Basketball Tennis
Favourite sports
Sports
Nu
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(ii) 6 + 3 + 2 + 5 + 8 + 6 = 30 (iv) 6 ___ 30 × 100 ____ 1 = 20%
(iii) Basketball (v) 3 ___ 30 = 1 ___ 10
Q. 8. (i) 1 + 2 + 4 + 5 + 7 + 5 + 2 + 1 + 1 = 28(ii) Six
(iii) 2 + 1 + 1 = 4
(iv) 7 ___ 28 × 100 ____ 1 = 25%
Exercise 1.5
Q. 1. (i) x = 360° � (180° + 60° + 45° + 45°)x = 30°
(ii) Bus = 180° _____ 360°
× 24 = 12
Train = Bicycle = 45° _____ 360°
× 24 = 3
Car = 60° _____ 360°
× 24 = 4
Walk = 24 × 180° _____ 360°
= 2
Mode Bus Car Train Walk Bicycle
Frequency 12 4 3 2 3
Q. 2. (i) x = 360° – (162° + 90° + 72°)x = 36°
(ii) Basketball = 162° _____ 360°
× 20 = 9
Tennis = 36° _____ 360°
× 20 = 2
Hurling = 72° _____ 360°
× 20 = 4
Soccer = 20 � (9 + 2 + 4) = 5
Sports Basketball Tennis Hurling Soccer
Number 9 2 4 5
(iii) Soccer: 5 ___ 20 × 100 ____ 1
= 25%
7
Q. 3. (i) Art = 360° – (150° + 45°) = 165°
(ii) Technology = 150° _____ 360°
× 120 = 50
Music = 45° _____ 360°
× 120 = 15
Art = 120 – (50 + 15) = 55
Subject Technology Music Art
Frequency 50 15 55
Q. 4. (i) Grazing = 360° – (144° + 30° + 60°) = 126°
(ii) Vegetables = 30° _____ 360°
= 1 ___ 12 of hand use
1 ___ 12 (hand) = 15 acres
� hand = 12 × 15 = 180 acres
(iii) Wheat = 60° _____ 360°
× 180 = 30 acres
Q. 5. (i) A = 72° _____ 360° = 1 __ 5
So 1 __ 5 of the class achieved an A
� 1 __ 5 (class) = 40
� class = 200
(ii) 144°
(iii) Percentage:
B = 108° ____ 360°
× 100 ____ 1
= 30%
C = 144° ____ 360°
× 100 ____ 1
= 40%
D = 100% – (20% + 30% + 40%)= 10%
Number:
B = 200 × 30% = 60
C = 200 × 40% = 80
D = 200 × 10% = 20
Grade A B C D
Number 40 60 80 20
Percentage 20% 30% 40% 10%
Q. 6. Step 1: Total = 20
Step 2: Girls: 5 ___ 20 × 360° = 90°
Boys: 15 ___ 20 × 360° = 270°
Step 3:
270º
Boys
Girls
90º
8
Q. 7. (i) German = 30 – (15 + 10) = 5Step 1: Total = 30
Step 2: French: 15 ___ 30 × 360° = 180°
Spanish: 10 ___ 30 × 360° = 120°
German: 5 ___ 30 × 360° = 60°
(ii) German: 5 ___ 30 × 100 ____ 1 = 16 2 __ 3 %
Q. 8.
75.6º
3.6º = Other gases
280.8º
Oxygen
Nitrogen
Nitrogen: 78% × 360° = 280.8°Oxygen: 21% × 360° = 75.6°Others: 1% × 360° = 3.6°
Exercise 1.6
Q. 1. (i) Stem Leaf
1
2
3
4
5
6
7
8
9
10
2
0, 6, 6, 8
2, 7
1
0, 1, 2, 2, 6, 7
6, 6, 6, 9
8
0 Key: 6|1 = 61%
(ii) 15 ___ 20 × 100 ____ 1 = 75%
Step 3:
60º
120º
French
Spanish
German
180º
Q. 2. Stem Leaf
5
6
7
8
9
1, 1, 5
0, 0, 0, 2, 3, 3, 7, 7, 9
0, 2, 2, 2, 3, 5, 6, 7, 7, 9
2, 3, 3, 9
0, 3, 7, 9 Key: 6|0 = 60
9
Q. 3. (i) Stem Leaf
13
14
15
16
17
18
8, 9
3, 8, 9, 9
3, 4, 4, 5, 6, 6, 7, 7, 8
5, 5, 5, 6, 8
5, 7, 8
1, 3 Key: 17|5 = 175 cm
(ii) There are 25 in the class.There are 5 + 3 + 2 = 10 taller
� 10 ___ 25 = 2 __ 5 fraction of the class taller
Q. 4. (i) 8 + 10 + 9 + 7 + 3 + 1 + 2 = 40
(ii) 3 + 1 + 2 = 6
(iii) 8 + 10 _______ 40 = 18 ___ 40 = 9 ___ 20
Q. 5. Ranked set:
10.5 10.6 10.7 10.8 11.0 11.1
11.2 11.2 11.5 11.6 11.8 12.0
12.2 12.3 12.3 12.5 12.5 12.7
13.1 13.1
(i) Stem Leaf
10
11
12
13
5, 6, 7, 8
0, 1, 2, 2, 5, 6, 8
0, 2, 3, 3, 5, 5, 7
1, 1 Key: 11|1 = 11.1 s
(ii) 4
(iii) 13.1 – 10.5 = 2.6 seconds
Q. 6. Ranked set:
13 13 13 15 19 19 20 21
24 27 28 31 32 32 32 34
42 45 46 48
(i) Stem Leaf
1
2
3
4
3, 3, 3, 5, 9, 9
0, 1, 4, 7, 8
1, 2, 2, 2, 4
2, 5, 6, 8 Key: 2|4 = 24
(ii) 6 Teenages � 14 not going to school
� 14 ___ 20 × 100 ____ 1 = 70%
10
Q. 7. (i) 3 + 4 + 5 + 2 + 1 = 15
(ii) 3 ___ 15 × 100 ____ 1 = 20%
Q. 8. (i) 46
(ii) 11 + 2(12) + 13 + 17 + 19 + 22 + 24 + 2(29) + 31 + 33 + 39 + 41 + 46 = 378
(iii) 375 × 2 __ 3 = 252
Q. 9. (i) 6 + 5 + 3 + 3 + 1 = 18
(ii) 1
(iii) Pulse rate increased after the run.
Q. 10. Men Women
9
8, 6, 1, 0
9, 9, 8, 6, 5, 5, 4, 4, 1, 0, 0
6, 5, 4, 3, 3, 1
1
14
15
16
17
18
19
8, 9
0, 1, 2, 3, 4, 5, 5, 7, 7, 8, 8
1, 2, 3, 5, 6, 7, 9
1, 4, 8
Key: 17|1 = 171 cm
Q. 11. (i) Male Female
8
8, 7
8, 8, 4, 1
7, 4
0
11
12
13
14
15
16
17
5
9
0, 1, 4, 6, 8
0
1, 1 Key: 16|0 = 160 cm
(ii) Male Female
5, 4, 4, 4, 4, 4, 4, 3, 2
Key: 2|4 = 24 cm 1
2
3
0, 1, 2, 2, 3, 4, 4
1, 1, 2
Exercise 1.7
Q. 1. Distance 0–2 2–4 4–6 6–8 8–10
Number 20 12 14 5 2
11
Q. 2. 16141210
8642
15 20 25 30 35 40
Fre
qu
en
cy
Age
Q. 3. Time (min) 0–1 1–2 2–3 3–4 4–5
Number 2 3 5 2 1
(i) 2 + 3 + 5 = 10
(ii) Total = 2 + 3+ 5 + 2 + 1 = 13
Percentage = 2 ___ 13 × 100 ____ 1 = 15.38%
Q. 4. (i)
161820
1412108642
0 3 6 9 12
Nu
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Time (hours)
Hours sleep
(ii) 20 + 15 = 35
(iii) 15
Q. 5. (i) 6
5
4
3
2
1
20 40 60 80 100
Fre
qu
en
cy
Time (minutes)
Time watching television
(ii) 2 ___ 20 × 100 ____ 1 = 10%
12
Q. 6. (i) Time (sec) 2–3 3–4 4–5 5–6 6–7
Number 3 4 5 2 1
(ii)
5
4
3
2
1
2 3 4 5 6 7
Nu
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Time (sec)
Time to answer question
Q. 7. (i) 87654321
5 10 15 20 3025
Nu
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Time (min)
(ii) 8 + 6 + 2 = 16
(iii) 6 + 2 = 8
Revision Exercises
Q. 1. (i) Handed Right Left Ambidextrous
Freq. 8 1 1
(ii) Total = 8 + 1 + 1 = 10
Right: 8 ___ 10 × 360° = 288°
Left = Ambidextrous = 1 ___ 10 × 360° = 36°
288º
Right
Left
Ambi.36º
36º
(iii) Tick the one that applies to you:
Right-handed Left-handed Ambidextrous
13
Q. 2. (i) Result 1 2 3 4 5
Frequency 4 2 7 3 4
(ii) 7654321
1 2 3 4 5Result
Fre
qu
en
cy
(iii) 4 (iv) 20 – 4 = 16, so 16 passed
Percentage = 16 ___ 20 × 100 ____ 1 = 80%
(v) 1: 4 ___ 20 × 360° = 72°
2: 2 ___ 20 × 360° = 36°
3: 7 ___ 20 × 360° = 126°
4: 3 ___ 20 × 360° = 54°
5: 4 ___ 20 × 360° = 72°
(vi) Bar chart because it gives the frequency on the y-axis; the pie chart does not give the frequency.
Q. 3. Primary sources: Surveys and questionnaires – The company could carry out surveys to see what content would be popular in teen magazines.
Secondary sources: Other teen magazines – The company could check other teen magazines to see the type of content they contain.
Q. 4. (i) Number 0 1 2 3 4
Tally |||| ||||| ||||||||||||||||||||||||||||||| |||| |||| |||||| || ||||||||||||||||||||||||||||||| |||| |||||||| || ||||
Frequency 6 7 4 1 2
(ii) 6 + 7 + 4 + 1 + 2 = 20
(iii) 0: 6 ___ 20 × 360° = 108°
1: 7 ___ 20 × 360° = 126°
2: 4 ___ 20 × 360° = 72°
3: 1 ___ 20 × 360° = 18°
4: 2 ___ 20 × 360° = 36°
1
2
3
4
5
72º72º54º
126º36º
0
3
4
2
1126º108º
72º18º
36º
14
(iv) 7 ___ 20 × 100 ____ 1 = 35%
(v) I would firstly find a list of all students in the school. (This list could be student names or student ID numbers.) This list is available in the office. Each student name would be assigned a number. (Again, office staff will be able to assign a number to each student.) Using a calculator or spreadsheet, generate 20 random numbers. These 20 numbers will generate your sample.
Q. 5. (i) 50454035302520151050
Mon Tue Wed Thu Fri Sat
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Day
(ii) 5 + 10 + 10 + 20 + 15 + 50 = 110
(iii) 50 ____ 110 = 5 ___ 11
(iv) Mean = 110 ____ 6 = 18 1 _ 3
(v) People have more time to read papers on Saturday because fewer people are at work. Also there’s more in Saturday papers (magazines and weekly television listings).
Q. 6. (i) Modes of transport
0
5
10
15
20
25
Walk Bus Cycle Car Train
Mode
Number
(ii) 5 + 20 + 6 + 2 + 1 = 34
(iii) BusIt may be the fastest mode of transport due to bus lanes or maybe a lot of people surveyed live far away from school.
15
(iv) Mode Walk Bus Cycle Car Train
Number 9 20 6 2 1
(v) Modes of transport
0
5
10
15
20
25
Walk Bus Cycle Car TrainMode
Number
Q. 7. (i) Number 1 2 3 4 5 6
Tally || |||||| |||||||| |||||| |||| |||| ||||| || |||||||||||||||||||||||||||||| ||||
Frequency 1 3 4 3 2 7
(ii) 1 + 3 + 5 + 3 + 3 + 5 = 20
(iii) Numbers guessed
123456
(iv) 6(v) 1
Q. 8. (i) Stem Leaf
1
2
3
0, 5, 6, 7, 8, 8, 8
0, 0, 0, 3, 4, 4, 5, 6, 8, 9
0, 2, 2, Key: 2|0 = 20
(ii) 10 + 15 + 16 + 17 + 3(18) + 3(20) + 23 + 2(24) + 25 + 26 + 28 + 29 + 30 + 2(32) = 445
16
(iii) 2 ___ 20 × 100 = 10%
(iv) 30 + 32 + 32 = 94
64 ____ 445 × 100 = 14%
Q. 9. (i) 18
16
14
12
10
8
6
4
2
20 30 40 50 60 70
Fre
qu
en
cy
Weight
(ii) 4 ___ 50 × 100 = 8%
Q. 10. (i) This is a not a reliable source because, in general, the majority of the sample would have purchased a computer. This is not a random sample.
(ii) This is not reliable because you have just tested one of the potatoes; it may be the smallest in the pot. However, if you tested the largest it would be reliable because it is the last to be fully cooked.
(iii) This is unreliable because the majority of customers would be well off and they would probably drive expensive cars.
(iv) The sample size is too small. The sample is probably of people the same age and the majority may be the same gender. Pocket money received usually varies with age and possibly gender.
Q. 11. (i) Student Stem Teacher
9, 8, 7
9, 9, 7, 7, 5, 5, 4, 4, 1
3, 2
0
2
3
4
5
6
9
5, 6, 8
1, 2, 2, 3, 3, 4, 5, 5, 5
6
1 Key: 4|2 = 42 seconds
(ii) 2 students from each year – 1 boy, 1 girl and 3 others. 15 teachers who teach different subjects and a good spread of ages.
(iii) You might end up with an uneven distribution of ages/genders/subjects taught. Sometimes people will not take part in tests such as this if they feel they will not perform well. In this question, it is possible that some slow texter’s have been omitted from the sample.
17
Q. 12. (i) Men Women
5
8, 5
8, 4
8, 6
6
0
2
3
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
7
0, 2
2, 5
0
1
0
(ii) Men are more likely to go to hardware stores, as they are more interested in DIY.
(iii) She will conclude that men will spend more money in shops than women. This is the question she set out to answer.
(iv) Julie only looked at one shop.
Men are more likely to shop in hardware stores.
Men are more likely to shop on Saturday morning.
(v) Look at a number of different shops over a longer period of time.
Q. 13. (i) 40 cm
(ii) 11 cm
(iii) 52 cm
(iv) 52 – 11 = 41 cm
(v) Location 2. It contains the highest tulips. This is evident from the stem-and-leaf diagram. Most measurements are towards the bottom of the Location 2 graph, whereas most measurements in the Location 1 graph are towards the top of the graph.
Q. 14. (i) Table 1 Table 2
9, 8, 8, 7, 6, 5, 5, 3, 2, 2
7, 4, 2, 0, 0
4
5
6
6, 6, 8, 8, 9
0, 0, 1, 1, 2, 5, 5, 6, 6, 8
Key: 5|0 = 5.0 cm
(ii) Table 1 contains male measurements. A representative sample of male wrist measurements would contain bigger measurements than a representative sample of female wrist measurements because in the population of males, wrist measurements are bigger than in the female population.
18
(iii) 5.8 cm
(iv) 6
(v) 5.2 cm
(vi) 9
Q. 15. (i) Males Females
6
8, 4, 4, 4, 4, 0, 0, 0
6, 6, 2, 2, 2
8, 8, 8, 4, 4
6
5
6
7
8
9
0, 4, 4, 8, 8, 8, 8
2, 2, 2, 2, 2, 6, 6
0, 0, 0, 8
6 Key: 6|4 = 64 beats/min
(ii) Yes. The shapes of the male stem and leaf diagram and the female stem and leaf diagram are both similar.
(iii) She could randomly select 20 households in the neighbourhood and ask a male and female volunteer (adult) from each household to allow her to measure their pulse rates.
(iv) 96 – 56 = 40 beats per minute
(v) 96 – 60 = 36 beats per minute
(vi) If any of her subjects had been exercising prior to the measurements, then this would lead to a higher pulse rate for that individual and hence would bias or distort the results. Some subjects may not agree to participate. This could be for a number of reasons. If the reason was medical, then it may be possible that the individual may have an unusual pulse rate and this would not be included in Alice’s results, leading to bias.
Q. 16. (i) Height (cm) 145.5–155.5 155.5–165.5 165.5–175.5 175.5–185.5
Tally |||||||| ||||||||||||||||||||||||||||||||||||||||||||||||| |||| ||||| ||||||||||||||||||||||||||| |||| ||||||||
Number 4 11 4 0
8
9
11
10
7
6
5
4
3
2
1
145.5 155.5 165.5 175.5 185.5Height (cm)
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19
(ii) Height (cm) 145.5–155.5 155.5–165.5 165.5–175.5 175.5–185.5
Tally || |||| ||||||||||||||||||||||||||||||||||||||||| ||||||||||||||||||||||||||||||||| |||||||||||||||||||||||||||||||||
Number 1 2 10 5
8
9
10
7
6
5
4
3
2
1
145.5 155.5 165.5 175.5 185.5Height (cm)
Nu
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(iii) The heights of both histograms are similar. The male histogram has a bigger base (more spread).
(iv) (a) The samples are being chosen from one passenger list. This cannot be representative of the whole population of people who use air travel. What if the flight was to a country in which the average height of the population was smaller than the global average?
(b) It is obvious from the table that some people may have refused to be measured. People who are conscious of their heights could possibly refuse and would not be represented.
