Download Extended-answer questions (90 MARKS)

REVISION ON UNIVARIATED DATA
QUESTIONS
MULTIPLE-CHOICE (43 MARKS)
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
8 marks
Total: 90 marks
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
2 marks
b
1
0
0
5
10
15
Test score
20
25
4 marks
2 a
2 marks
b Q1= 58 , M = 61 , Q3 = 69
2 marks
c i
58, 69
ii 58
2 marks
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 marks
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
3 marks
b positively skewed with an outlier
2 marks
c 55–59
1 mark
d 11/19 or 57.9%
2 marks
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.
3 marks
5 a
Lunch
preference
Wrap
Salad
Pie
Total
Frequency
Count
10
7
13
30
Percent
33.3
23.3
43.3
99.9
2 marks
b
45
40
30
25
20
e
Percentage
35
15
10
5
0
Pie
Wrap
Lunch preference
Salad
2 marks
Total: 30 marks
6 a median; positively skewed distribution with possible outliers
2 marks
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).
2 marks
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
2 marks
b Hop, step and jump; her performance is in the top 2.5% of performances in the club
1 mark
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
8 marks
Total: 90 marks