Download Univariate Data: Revision Exercises

Essential Standard General Mathematics Teacher CD-ROM
Chapter 1 Univariate data: Revision sheet
Short-answer
1 Classify the following data as categorical or numerical:
a the number of bedrooms in a house
b attitude to mandatory detention for illegal immigrants on a scale of 1 to 5, where
1 = strongly agree, 2 = agree, 3 = neither agree nor disagree, 4 = disagree and
5 = strongly disagree
c result on a mathematics exam expressed as A, B, C, D, or E
d score out of 100 on a mathematics exam
e salary in dollars
f salary expressed as ‘above average’, ‘average’ or ‘below average’
2 The following bar chart shows the percentage of cars of each colour observed in a car
yard:
a What is the level of measurement of car colour?
b What percentage of cars in the car yard are blue?
3 A researcher asked a group of people to record how many cups of coffee they drank in a
week. Here are her results:
0
0
9
12
15
0
35
41
4
12
11
2
4
15
16
53
32
9
4
11
21
15
a Using class intervals 0–9, 10–19, etc. construct a histogram of this data.
b Construct a cumulative frequency distribution for this data.
© Jones, Lipson, Main, Tulloch 2006
1
Essential Standard General Mathematics Teacher CD-ROM
Chapter 1 Univariate data: Revision sheet
4 The marks awarded to a group of students on an assignment are as follows:
10
11
12
12
15
9
8
11
14
14
12
11
12
14
15
16
17
19
Construct a dot plot of this data.
5 The amounts (to the nearest dollar) that a group of people spend on entertainment each
week are given below:
100
71
42
12
15
19
83
110
145
54
122
115
212
55
32
16
95
78
Find the mean and standard deviation, the median and the interquartile range, and the
range of these amounts.
6 In a study of the use of mobile phones, a researcher recorded the number of phone calls
received in a week by each of a group of volunteers. Her results are summarised in the
following five number summary:
Min = 3
Q1 = 12
M = 23
Q3 = 56
Max = 100
Use the five number summary to construct a boxplot of this data.
7 A group of former company managers was asked to give their age when officially retiring
from full-time work. The resulting data is given below.
70
74
60
72
65
49
71
75
57
55
65
70
59
77
67
80
60
63
a Construct a boxplot of the retirement ages.
b What was the median age of retirement for this sample of workers?
© Jones, Lipson, Main, Tulloch 2006
2
Essential Standard General Mathematics Teacher CD-ROM
Chapter 1 Univariate data: Revision sheet
Extended-response
1 A ‘do-it-yourself’ furniture manufacturer wants to determine how easily a new prepacked
TV cabinet can be put together by their customers. They chose 45 customers and tested
how long it took each of them to construct the cabinet. The number of minutes taken to
build each cabinet is shown below.
14
19
32
32
22
29
36
36
34
37
37
32
31
28
18
36
33
23
24
32
29
29
24
36
24
35
23
19
37
29
18
32
15
28
38
28
36
36
33
38
35
28
33
35
32
a Construct a histogram for the time taken to put the cabinet together, using class
intervals 10 – <15, 15 – <20, etc.
b What is the shape of the distribution?
c What percentage of customers took less than 30 minutes to build the cabinet?
d What percentage of customers took 15 minutes or longer to build the cabinet?
e Calculate the mean and the standard deviation for the construction times.
The cabinet is available in both standard and deluxe models. The data given above refers to
the standard model. The following table gives the time to assemble the cabinet for a sample of
deluxe cabinets:
23
31
50
50
35
46
56
56
53
58
58
50
49
44
29
56
52
44
38
35
46
38
38
56
38
55
37
31
28
46
29
50
19
44
59
44
56
56
52
59
f Construct boxplots for the construction times of both the deluxe cabinet and the
standard cabinet on the same axes.
g Use the information from the boxplots to compare the distribution of construction times
for the two types of cabinets in terms of shape, centre and spread.
© Jones, Lipson, Main, Tulloch 2006
3
Essential Standard General Mathematics Teacher CD-ROM
Chapter 1 Univariate data: Revision sheet
Chapter 1 Revision sheet answers
Short-answer
1 a numerical
b categorical
c categorical
d numerical
e numerical
f categorical
2 a categorical
b 14%
3 a
b
4
© Jones, Lipson, Main, Tulloch 2006
4
Essential Standard General Mathematics Teacher CD-ROM
Chapter 1 Univariate data: Revision sheet
5 mean = $76.44
standard deviation = $53.00
median = $74.50
IQR = $78.00
range = $200
6
7 a
b 66 years
© Jones, Lipson, Main, Tulloch 2006
5
Essential Standard General Mathematics Teacher CD-ROM
Chapter 1 Univariate data: Revision sheet
Extended-response
1 a
b negatively skewed
c 44.4%
d 97.8%
e mean = 29.67 mins, stand dev = 6.62 mins
f
g The distribution of times to assemble both the deluxe and the standard cabinets are
negatively skewed. In general, the standard cabinet (median = 32 minutes) is much
more quickly assembled than the deluxe cabinet (median = 46 minutes). The time to
assemble the deluxe cabinet is more variable (IQR = 18 minutes) than the time to
assemble the standard cabinet (IQR = 11.5 minutes).
© Jones, Lipson, Main, Tulloch 2006
6