Download Extended-answer questions (90 MARKS)

REVISION ON UNIVARIATED DATA
QUESTIONS
MULTIPLE-CHOICE
The following information relates to Questions 1 to 2
Two hundred people were asked about their attitude to compulsory voting
(support, no opinion, do not support) and their age (in years).
1 The variables Attitude to compulsory voting and Age are:
A both categorical variables
B both numerical variables
C a categorical and a numerical variable respectively
D a numerical and a categorical variable respectively
E neither numerical nor categorical variables
2 The most appropriate way to graphically display the information about Age is to use a:
A dot plot
B bar chart
C histogram
D segmented bar chart
E back-to-back stem plot
3 The variable number of people at a rock concert is a:
A a continuous numerical variable
B a discrete numerical variable
C a continuous categorical variable
D a discrete categorical variable
E none of the above
The following information relates to Questions 4 and 5
The responses of the two hundred people who were asked about their attitude to
compulsory voting have been organised into a frequency table as shown below.
Some information is missing.
Attitude to compulsory
voting
Support
No opinion
Frequency
Count Percentage
153
10.0
Do not support
27
Total
200
100.0
4 The percentage of people who supported compulsory voting is:
A 10.0%
B 15.3%
C 27.0%
D 76.5%
E 90.0%
5 The number of people who had no opinion is:
A 10
B 15
C 20
D 27
E 200
Questions 6 to 9 relate to the histogram shown below
The age distribution for the population of Sassafras in 1986 is shown below
25
percentage
20
15
10
5
0
0
10
20
30
40
50
60
70
80
90
age
6 The percentage of the people in Sassafras who were aged 20 to 29 years in 1986 was closest
to:
A 9%
B 14%
C 18%
D 20%
E 29%
7 The percentage of people in Sassafras who were aged less than 20 years in 1986 was closest
to:
A 15%
B 19%
C 20%
D 24%
E 34%
8 In 1986, 1459 people lived in Sassafras. The number of residents under ten years of age was
closest to:
A 19
B 146
C 186
D 277
E 729
9 The centre of the distribution lies between:
A 10 and 20
B 20 and 30
C 30 and 40
D 40 and 50
E 50 and 60
10 For the distribution displayed by stem plot below, the range is:
3
3
4
4
5
1
5
3
5
4
2
6
3
9
3
3
4
4
4
4
A 3
B 10
C 23
D 25
E 54
11 For the distribution displayed by stem plot below, the centre is:
3
3
4
4
5
A 5
B 6
C 34
1
5
3
5
4
2
6
3
9
3
4
3
4
4
4
D 35
E 36
Questions 12 and 13 relate to the segmented bar chart below
The percentage segmented bar chart below shows the distribution of fast food
preferences of 200 students.
100
Other
90
80
Pizza
Percentage
70
Chinese
60
Fish & chips
50
40
Chicken
30
Hamburgers
20
10
0
Fast food preference
12 The number of students who preferred Pizza is closest to:
A 27
B 52
C 66
D 122
E 176
13 For these 200 students, the most popular fast food is:
A Chicken
B Chinese
C Fish & chips
D Hamburgers
E Pizza
14 The subject choices of VCE students in a large school were recorded. The best graph to
display this information would be a:
A bar chart
B dot plot
C histogram
D stem plot
E back-to-back stem plot
The following information relates to Questions15 to 17
The following is a set of test marks:
10, 14, 23, 5, 16, 12, 8, 11, 12, 13, 15
15 The median value is:
A 10
B 11
C 12
D 12.5
E 13
16 The first quartile is:
A 9
B 10
C 11
D 12
E 12.5
17 The range is:
A 5
B 12
C 15
D 18
E 23
The following information relates to Questions 18 to 19
The following is an ordered set of sapling height (in cm):
198, 208, 210, 211, 212, 213, 214, 215, 216, 218
18 The median value is:
A 211.5 cm
B 212 cm
C 212.5 cm
D 213 cm
E 213.5 cm
19 The interquartile range (IQR) is:
A 5 cm
B 6 cm
C 7 cm
D 8 cm
E 9 cm
20 The following is a set of 10 daily minimum temperatures (in degrees Celsius):
5, 6, 8, 4, 9, 9, 8, 7, 6, 10
The five-number summary for these temperatures is:
A 4, 6, 7.5, 9, 10
B 4, 6, 7, 9, 10
C 4, 6, 8, 9, 10
D 4, 5.5, 7.5, 8.5, 10
E 4, 5.5, 7.5, 8, 10
The following information relates to Questions 21 to 29
A
B
1
0
0
5 10 15 20 25 30 35 40 45 50
C
1
0
0
5 10 15 20 25 30 35 40 45 50
0
5 10 15 20 25 30 35 40 45 50
D
1
0
1
0
0
5 10 15 20 25 30 35 40 45 50
0
5 10 15 20 25 30 35 40 45 50
E
1
0
21 The median of box plot D is closest to:
A 20
B 25
C 27
D 29
E 30
22 The IQR of box plot B is closest to:
A 5
B 10
C 15
D 20
E 44
23 The range of box plot C is closest to:
A 5
B 10
C 20
D 25
E 45
24 The description that best matches box plot A is:
A symmetric
B positively skewed
C positively skewed with outliers
D negatively skewed
E negatively skewed with an outlier
25 The description that best matches box plot B is:
A symmetric
B negatively skewed with an outlier
C negatively skewed
D positively skewed
E positively skewed with an outlier
26 The description that best matches box plot C is:
A symmetric
B symmetric with outliers
C negatively skewed with outliers
D positively skewed
E positively skewed with outliers
27 The description that best matches box plot D is:
A symmetric
B symmetric with outliers
C negatively skewed
D positively skewed
E positively skewed with outliers
28 The description that best matches Box Plot E is:
A symmetric
B symmetric with outliers
C negatively skewed
D positively skewed
E positively skewed with outliers
29 For Plot C, outliers in the upper tail are defined as data values that are:
A greater than 15
B greater than 20
C greater than 25
D greater than 30
E greater than 40
The following information relates to Questions 30 to 31
The following is a set of measurements:
11.0, 11.4, 12.3, 10.5, 11.6, 11.2, 11.8, 11.1, 11.2, 11.3, 11.5
30 The mean value is closest to:
A 11.1
B 11.15
C 11.35
D 11.50
E 11.56
31 Correct to two decimal places, the actual value of the standard deviation is:
A 0.42
B 0.44
C 0.46
D 0.48
E 0.50
32 The mean of a data distribution is best described as:
A the average
B the middle value
C the central value
D the balance point
E the middle 50% of values
33 It would not be appropriate to determine the mean and standard deviation of a group of
people’s:
A salary
B thigh length
C years of schooling
D school type
E number of hours worked each week
34 It is reasonable to use the mean measure of the centre of a distribution:
A when the distribution is negatively skewed
B when the distribution is positively skewed
C when the distribution is symmetric
D when the distribution is symmetric with outliers
E always
35 A student’s mark on a test is 75. The mean mark for their class is 68 and the standard
deviation is 4. Their standardised score is:
A –2.5
B –1.75
C 0
D 1.75
E 2.5
36 A student’s standardised score on a test is –0.5. The mean mark for their class is 68 and the
standard deviation is 4. Their test score is:
A 60
B 64
C 66
D 67.5
E 70
In Questions 37 to 40, SD is used as an abbreviation for standard deviation
37 In a normal distribution, approximately 95% of values lie:
A within one SD of the mean
B within two SDs of the mean
C within three SDs of the mean
D more than one SD above the mean
E more than two SDs below the mean
38 In a normal distribution, approximately 0.3% of values lie:
A within one SD of the mean
B within two SDs of the mean
C within three SDs of the mean
D more than three SDs above or below the mean
E more than two SDs above or below the mean
39 In a normal distribution, approximately 2.5% of values lie:
A within one SD of the mean
B within two SDs of the mean
C within three SDs of the mean
D more than one SD above the mean
E more than two SDs above the mean
40 In a normal distribution, approximately 32% of values lie:
A within one SD of the mean
B within two SDs of the mean
C within three SDs of the mean
D more than one SD above or below the mean
E more than two SDs above or below the mean
The following information relates to Questions 41 to 43
The heights of a group of 256 junior athletes is approximately normally distributed with a mean
of 157 cm and a standard deviation of 3 cm.
41 The percentage of the junior athletes with heights between 148 and 166 cm is:
A 0.03%
B 50%
C 68%
D 95%
E 99.7%
42 The number of junior athletes with heights less than 151 cm is around:
A 3
B 6
C 12
D 128
E 250
43 The number of junior athletes with heights greater than 154 cm is around:
A 82
B 128
C 175
D 215
E 250
Extended-answer questions (90 MARKS)
Show answers and any working in the spaces provided. Marks are given for correct
and clearly set out working and answers.
1 The five number summary for a set of 33 test scores is: 4, 8, 12, 16, 20.
a Write down the range and the interquartile range of the 33 test scores.
2 marks
b Use the five number summary to draw a box plot with a suitably scaled and labeled axis.
4 marks
2 The strike rates (runs/100 balls) of 19 one-day cricketers are given below.
70, 63, 59, 66, 54, 69, 64, 72, 61, 54, 85, 59, 58, 57, 58, 69, 91, 58, 61
a Use your calculator to construct an box plot (with outliers) for the data.
2 marks
b Use the box plot to locate the median and the quartiles, Q1 and Q3.
2 marks
c Complete the following statements:
i
The middle 50% of the one-day cricketers had a strike rate between ______ runs/100
balls and _____ runs/100 balls.
ii 75% of the one-day cricket players had a strike rate greater than _____ runs/100 balls.
2 marks
d Write a brief report using the box plot to describe the distribution of the strike rate for
these cricketers in terms of shape, centre, spread and outliers. Give appropriate values.
3 marks
Total: 30 marks
3
The strike rates (runs/100 balls) of 19 one-day cricketers are given below.
70, 63, 59, 66, 54, 69, 64, 72, 61, 54, 75, 59, 58, 57, 58, 69, 91, 58, 61
a Construct an ordered stem plot with the stems split in two.
3 marks
b Describe the shape of the distribution.
2 marks
c Determine the modal interval.
1 mark
d Determine the percentage of these cricketers with strike rates above 60 runs/100 balls.
2 marks
4 The distribution of ages for the population of Australia in 1986 is shown in the histogram
below. Use the histogram to help you complete the report on the distribution of ages in terms
of shape, centre and spread.
18
16
percentage
14
12
10
8
6
4
2
0
10
20
30
40
50
age
60
70
80
90
100
Report: The distribution of ages of the population of Australia in 1986 is ____________.
There are no outliers. The centre of the age distribution is approximately ____ years. The
distribution has a spread of approximately ____ years.
3 marks
5 The lunch choices of 30 students were recorded as ‘W’ for wrap, ‘S’ for salad and ‘P’ for pie,
as shown below.
S
P
W
S
P
W
W
S
P
P
W
P
P
W
P
S
W
P
P
P
S
W
P
W
W
P
S
S
P
W
a Use the data to complete the table below.
Lunch
preference
Frequency
Count
Percent
Wrap
Salad
Pie
Total
2 marks
b Use the table to construct a percentage frequency bar chart for the data.
2 marks
6 The stem plot below shows the distribution of strike rates (runs/100 balls) for 18 one-day
cricketers.
5
5
6
6
7
7
8
8
9
Strike rate
4 4
7 8 8 9 9
1 1 3 3 4
6 9
0 2
5
1
a From the shape of the distribution, which measure of centre, the mean or the median, do
you think would best indicate the typical strike rate of these cricketers? Explain your
decision.
2 marks
b Calculate both the mean and median and check your prediction.
2 marks
7 A young athlete competes in three events at her club: the long jump, the high jump and the
hop, step and jump.
a Complete the table by calculating standard scores for each of her events.
Event
Long jump
High jump
Hop, step and
jump
Distance
/height (m)
4.85
1.57
Mean
4.75
1.58
Standard
deviation
0.3
0.05
6.45
5.92
0.25
Standardised score
2 marks
b Assuming that club member’s performance in each of the three events is approximately
normally distributed, in which event did she perform most strongly compared to her club
mates and why?
1 mark
8 The amount of time taken by a call centre to process a call is approximately normally
distributed with a mean of 3.5 minutes and a standard deviation of one minute. From this
information we can conclude that:
a 95% of calls will take between ______ and ______ minutes to process
b ______ % of calls will take less that 3.5 minutes to process
c ______ % of calls will take more than 2.5 minutes to process
d ______ % of calls will take more than 6.5 minutes to process
e around two thirds of calls will take between ______ and ______ minutes to process
f ______ % of calls will take less than 5.5 minutes to process
g ______ % of calls will take less than 30 seconds to process
h if a calls takes 3 minutes to process, then the call has taken (above/below) ______ the
average time to process
9.The table below gives the age distribution of the residents of Sassafras, a small settlement in the
Dandenong Ranges, in 1991.
Age
Males
0–9
10–19
20–29
30–39
40–49
50–59
60–69
70–79
80–89
90–99
Total
144
119
75
160
129
72
49
Percentage
males
18.6
9
0
774
Females
9.7
20.7
9.3
6.3
2.2
0
100.1
139
101
59
152
130
Percentage
females
19.3
43
30
7
0
721
Percentage
total
21.1
18.0
8.3
6.0
4.2
14.7
9.0
20.9
17.3
8.8
6.2
3.1
0
100.1
0
100.0
(Source: Shire of Yarra Ranges, 1995)
a How many people lived in Sassafras in 1991?
b Complete the table.
c In 1991, what percentage of the residents of Sassafras were:
i
aged between 40 and 49?
ii less than 50 years of age?
d In 1991, what percentage of the female residents of Sassafras were:
i
aged between 60 and 69?
ii aged between 30 and 79?
iii under 10 years of age?
iv 60 years of age or more?
e In 1991, what percentage of the male residents of Sassafras were:
i
aged between 20 and 29?
ii older than 49 and younger than 80?
iii under 40 years of age?
f Use the frequency table to construct a percentage histogram of the age distribution of the
residents of Sassafras in 1991.
g The age distribution for the population of Australia in 1986 is shown below. In what way
are the two age distributions similar, and in what way do they differ?
18
16
14
percentage
12
10
8
6
4
2
0
10
20
30
40
50
age
60
70
80
90
100
10 The table below displays a famous data set in statistics. It shows the distribution of chest sizes
(in inches) of 5738 Scottish Militiamen measured in the early 19th century.
Chest size
(inches)
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
Total
Frequency
3
18
81
185
420
749
1073
1079
934
658
370
92
50
21
4
1
5738
Percentage
0.0
0.3
1.4
3.2
13.0
18.7
18.8
11.5
6.5
1.6
0.9
0.0
99.9
Cumulative
percentage
0.0
0.3
1.7
4.9
12.2
43.9
62.7
79.0
90.5
98.6
99.5
99.9
99.9
a Complete the table by calculating the missing percentages and cumulative percentages
correct to one decimal place.
b What percentage of the soldiers have a chest measurement of :
i
less than 36 inches?
ii less than or equal to 38 inches?
iii more than 44 inches?
iv between 34 and 46 inches (inclusive)?
v between 38 and 42 inches (inclusive)?
c Use the information in the frequency table to construct a percentage frequency histogram
to display the distribution of chest sizes of the militiamen. Comment on features of the
distribution such a shape, centre and spread.
d In what ways do you think that the distribution of chest sizes of soldiers today would be
similar to that of nineteenth century Scottish Militia men, and in what way would you
expect it to differ?
e Show that the mean chest size of the Scottish militia men was 39.8 inches with a standard
deviation of 2.0 inches (correct to 1 decimal place).
f The distribution of chest sizes is approximately normal. Using the mean and standard
deviation as given above, check that the 68–95–99.7% rule holds approximately for this
data.
11 The table below lists the top 20 run-scorers in the old World Series Cricket. It shows the
number of innings, the strike rate (the number of runs scored per 100 balls) and the batsmen’s
average score (number of runs per innings). The data was compiled in 1996.
Name
Border (Aus)
Jones (Aus)
Boon (Aus)
Haynes (WI)
Richards (WI)
Marsh (Aus)
S. Waugh (Aus)
Greenidge (WI)
M. Waugh (Aus)
Taylor (Aus)
Wright (NZ)
Richardson (WI)
G. Chappell (Aus)
Wood (Aus)
Innings
160
90
91
83
60
64
88
39
58
44
53
62
48
44
Strike Rate
31
70
63
59
85
54
69
64
72
61
54
56
75
59
Average
31
47
37
37
47
36
30
43
28
34
29
27
35
37
Miandad (Pak)
Wessels (Aus)
Hughes (Aus)
Lloyd (WI)
Crowe (NZ)
Gower (Eng)
43
35
53
35
29
31
58
57
68
81
67
85
31
35
23
46
36
34
(Source: World Series 1996-97 Official Program)
For the variables Innings, Strike Rate and Average:
a construct a stem plot using split stems where appropriate.
b construct a box plot with possible outliers if appropriate.
c determine which cricketers stood out from the rest (outliers) for each variable.
12 The table below lists the life expectancies of males and females in 16 countries.
Country
Argentina
Bangladesh
Brazil
Canada
China
Colombia
Egypt
Ethiopia
France
Germany
India
Indonesia
Iran
Italy
Japan
Kenya
Life expectancy (Years)
Female
Male
74
67
53
54
68
62
80
73
72
68
74
68
61
60
53
50
82
74
79
73
58
57
63
59
65
64
82
75
82
76
63
59
a Complete a five-number summary for the life expectancies of females and males and
record your results in tabular form as shown below.
Five-number summary
Females
Minimum
First quartile
Median
Third quartile
Males
Maximum
b Use the five-number summaries to construct, on the same scale, a pair of box plots: one for
females and the other for males. Use the box plots to compare the distribution of life
expectancies of females and males in terms of shape (symmetric/skewed), outliers (if
any—identify), typical values (centre—quote appropriate values) and variability (spread—
quote appropriate values).
c Calculate the mean and standard deviation of life expectancy for both females and males.
Does the mean life expectancy give a reasonable indication of the typical life expectancy
of men and women in these countries? Explain.
13 The table below shows the weights carried by the horses in the Class 2 Handicap at a country
race meeting.
Horse
Gold Time
Malvern
Mutual Obsession
Retain
Gold Command
Our Charlie Boy
Simply Salubrious
Red Troubador
Hurricane Bob
Bisconic
Call Me
Melarno
Shining Prospect
It's Crunch Time
Boortkoi
Weight (kg)
58.0
58.0
57.0
56.5
55.5
55.5
55.5
55.0
54.5
54.0
53.5
53.5
53.5
52.5
52.5
a Complete a five-number summary for the weights carried by the horses and record your
results in tabular form as shown below.
Five-number summary
Weight
Minimum
First quartile
Median
Third quartile
Maximum
b What is the interquartile range?
c Use the five-number summary to construct a box plot for the data, with outliers if
appropriate.
d Use the information contained in the box plot to comment on the distribution of weights
carried by the horses in this race. Is the distribution approximately symmetric or is it
skewed? Are there any apparent outliers?
e i
Calculate the mean and the standard deviation of the weights carried by the horses
in this race. Give your answer correct to 1 decimal place.
ii Is it appropriate to use the mean as an indicator of a typical weight carried by the horses
in this race? Explain.
14 The data below gives the wrist circumference (in cm) of 15 men.
16.9
17.6
17.3
17.7
19.3
16.5
18.5
17.0
18.2
17.2
18.4
17.6
19.9
16.7
17.1
a Construct a box plot showing possible outliers if appropriate.
b Use the box plot to describe the distribution of wrist circumference for these men in terms
of shape (symmetric or skewed), outliers, typical wrist circumference (centre – with an
appropriate value) and variability of wrist circumferences (spread – with appropriate
values).
c Estimate the mean and standard deviation for the men's wrist circumferences.
d Calculate the mean and standard deviation for the men's wrist circumferences. Give your
answer correct to one decimal place.
e Are the mean and standard deviation appropriate measures of centre and spread for this
data? Explain.
Answers
Multiple-choice questions
1 C
2 C
3 B
4 D
5 C
6 A
7 E
8 D
9 C
10 C
11 D
12 B
13 D
14 A
15 C
16 B
17 D
18 C
19 A
20 A
21 B
22 D
23 E
24 E
25 D
26 B
27 A
28 E
29 D
30 C
31 C
32 D
33 D
34 C
35 D
36 C
37 B
38 D
39 E
40 D
41 E
42 B
43 D
Extended-answer questions
1 a R = 16, IQR = 8
b
1
0
0
5
10
15
Test score
20
25
2 a
b Q1= 58 , M = 61 , Q3 = 69
c i
58, 69
ii 58
d The distribution of strike rates is positively skewed with an outlier. The distribution is
centred at 61 runs/100 balls. The spread of the distribution as measured by the IQR is 11
runs/100 balls, and as measured by the range, 37 runs/100 balls. The outlier is a strike rate
of 91 runs/100 balls.
3 a
5
5
6
6
7
7
8
8
9
4
7
1
6
0
5
4
8
1
9
2
8
3
9
8
4
9
9
1
b positively skewed with an outlier
c 55–59
d 11/19 or 57.9%
4 Report: The distribution of ages of the population of Australia in 1986 is positively skewed.
There are no outliers. The centre of the age distribution is approximately 30 years. The
distribution has a spread of approximately 100 years.
5 a
Lunch
preference
Wrap
Salad
Pie
Total
Frequency
Count
10
7
13
30
Percent
33.3
23.3
43.3
99.9
b
45
40
30
25
20
e
Percentage
35
15
10
5
0
Pie
Wrap
Lunch preference
Salad
6 a median; positively skewed distribution with possible outliers
b median = 62 runs/100 balls; mean = 64.7 runs/100 balls (only 2/3rds of the cricketers have
strike rates less than the mean).
7 a
Event
Distance
Mean
Standard deviation Standardised score
/height (m)
Long jump
3.41
3.22
0.21
0.33
High jump
1.65
1.54
0.05
–0.2
Hop, step and jump
4.23
4.32
0.25
2.1
b Hop, step and jump; her performance is in the top 2.5% of performances in the club
8 a 1.5 and 5.5 minutes
b 50%
c 84%
d 0.15%
e 2.5 and 4.5 minutes
f 97.5 %
g 0.15%
h below average
9 a 1495
b
Age
0-9
10–19
20–29
30–39
40–49
Males
144
119
75
160
129
Percentage
males
18.6
15.4
9.7
20.7
16.7
Females
139
101
59
152
130
Percentage
females
19.3
14.0
8.2
21.1
18.0
Percentage
total
18.9
14.7
9.0
20.9
17.3
50–59
60–69
70–79
80–89
90–99
Total
c i
72
49
17
9
0
774
9.3
6.3
2.2
1.2
0
100.1
60
43
30
7
0
721
8.3
6.0
4.2
1.0
0
100.1
17.3
ii 80.8
d i
6.0
ii 57.6
iii 19.3
iv 11.2
e i
9.7
ii 17.8
iii 64.4
f
25
percentage
20
15
10
5
0
0
80
10
90
20
30
40
age
50
60
70
8.8
6.2
3.1
1.1
0
100.0
g Both the age distributions are positively skewed. However, the age distribution of the
residents of Sassafras has proportionally more people in the 0–9 year old age group, 19%
to 15% and the 30–39 year old age group, 21% to 16%, but proportionately less in the 20–
29 year old age group, 9% to 16%. From 50 years of age on, the two distributions tail off in
a similar manner.
10 a
Chest size
(inches)
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
Total
b i
1.7
ii 25.2
iii 1.3
iv 99.9%
v 78.3%
c
Frequency
3
18
81
185
420
749
1073
1079
934
658
370
92
50
21
4
1
5738
Percentage
0.0
0.3
1.4
3.2
7.3
13.0
18.7
18.8
16.3
11.5
6.5
1.6
0.9
0.4
0.0
0.0
99.9
Cumulative
Percentage
0.0
0.3
1.7
4.9
12.2
25.2
43.9
62.7
79.0
90.5
97.0
98.6
99.5
99.9
99.9
99.9
20
18
16
percentage
14
12
10
8
6
4
2
0
35
40
45
chest size (inches)
The distribution of chest sizes is symmetric (and bell shaped) and centred around 40
inches. Almost all chest measurements lie between 34 and 46 inches, with around 80%
lying between 38 and 42 inches.
d Similar shaped distribution but shifted to the right: people today tend to be larger on
average than people 200 years ago.
e answer given in question
f Percentage between 37.8 and 41.8 (1 standard deviation) = 66.8%
Percentage between 35.8 and 43.8 (2 standard deviations) = 95.3%
11 a
1
2
9
3
1559
4
3448
5
338
6
024
7
8
38
9
01
10
11
12
13
14
15
16 0
Innings
3
4
5
6
7
8
1
4467899
134789
025
155
Strike rate (runs/100
2
2
3
3
4
4
3
789
01144
5566777
3
677
Average(runs/innings)
balls)
b
41
73.5
0
91
29 53
innings
160
s
54 57.5 71
0
31
85
63.5
strike rate (runs/100 balls)
balls)
30.5
23
5
3
7
47
0
46
35
average (runs/innings)
(runs/innings)
c Innings:
Border stands out in terms of the exceptionally large number of innings he played
Strike rate: Border again stands out because his strike rate was very much lower than the
rest
Average: Jones and Richards because their average is sufficiently high for them to stand
out from the rest
12
a
Five-number summary
Minimum
First quartile
Median
Third quartile
Maximum
Females
Males
53
62
70
79.5
82
50
59
65.5
73
76
b
Female
Male
60
50
40
70
80
90
life expectancy (years)
120
Both distributions are symmetric, there are no outliers. The typical life expectancy of
females, Mfemales = 70 years, is higher than that of the males, Mmales = 65.5. There is more
variation in the female life expectancies. The females have a life expectancy range of 29
years and an IQR of 17.5 years. The males have a life expectancy range of 26 years and an
IQR of 14 years.
c Female: mean = 69.3; standard deviation = 10.2
Male:
mean = 64.9; standard deviation = 8.0
Yes, because both distributions are roughly symmetric (note that there is little difference
between the mean and medians).
13 a
Five-number summary
Weight
Minimum
First quartile
Median
Third quartile
Maximum
52.5
53.5
55
56.5
58
b IQR = 3
c
52
53
54
55
56
57
weight (kg)
d Distribution is symmetric with no apparent outliers.
58
59
e i
Mean = 55.0 SD = 1.8
ii Yes: The distribution is symmetric and there are no apparent outliers
14 a
17
16
18
wrist circumference (cm)
19
20
b Wrist circumference is approximately symmetrically distributed. The typical wrist size is
17.6 cm (if we use the median). Wrist circumferences range from 16.5 cm to 19.9 cm, and
the middle 50% of wrist circumferences lies between 17.0 and 18.4 cm.
c Estimated mean is around 18 cm.
Estimated standard deviation is around 1.0 cm:
19.9  16.5
 0.9
4
d Calculated mean = 17.7 cm
Calculated standard deviation = 1.0 cm
e Yes, distribution of wrist circumferences is approximatc
20
18
16
percentage
14
12
10
8
6
4
2
0
35
40
45
chest size (inches)
The distribution of chest sizes is symmetric (and bell shaped) and centred around 40
inches. Almost all chest measurements lie between 34 an