STAT20029 (T2,2020) Questions:
Week 2
Activity 1
Calculate appropriate class width for the following Per capita GDP data and form the frequency distribution:
Review Problem 2.8
RP2.8: A company manufactures a metal ring, which usually weighs about 1.4 kg, for industrial engines. A random sample of 50 of these metal rings produced the following weights (in kg). Construct a frequency distribution for these data using FIVE classes. What can you observe about the data from the frequency distribution?
1.51 |
1.59 |
1.42 |
1.25 |
1.34 |
1.51 |
1.51 |
1.19 |
1.62 |
1.31 |
1.56 |
1.16 |
1.25 |
1.48 |
1.59 |
1.42 |
1.62 |
1.25 |
1.31 |
1.16 |
1.48 |
1.96 |
1.51 |
1.62 |
1.45 |
1.53 |
1.79 |
1.19 |
1.34 |
1.34 |
1.48 |
1.51 |
1.31 |
1.02 |
1.65 |
1.45 |
1.08 |
1.39 |
1.42 |
1.76 |
1.11 |
1.25 |
1.56 |
1.22 |
1.48 |
1.22 |
1.19 |
1.62 |
1.39 |
1.45 |
Practice Problem 2.4
PP2.4: The human resources manager for a large company commissions a study in which the employment records of 500 company employees are examined for absenteeism (days off work) during the past year. The consultant conducting the study organises the data into a frequency distribution, shown below, to assist the human resources manager in analysing the data. For each class of the frequency distribution, determine the class midpoint, relative frequency and cumulative frequency.
Class interval |
Frequency |
(0, 2] |
218 |
(2, 4] |
207 |
(4, 6] |
56 |
(6, 8] |
11 |
(8, 10] |
8 |
Practice Problem 2.9
PP2-9: Construct a stem and leaf plot using two digits for the stem.
Practice Problem 2.14
PP2.14: The following data are monthly downloads (megabytes) on a handheld device. Construct a stem and leaf plot of the data, using whole part for the stem and the decimal part for the leaf. What does this plot tell you about monthly downloads on handheld devices?
Activity 2:
A sample of 29 factory workers were asked as to how long does it take each to travel from home to work on average. The following table provides their answers in minutes.
50 30 73 79 5 9
42 10 15 35 51 68
69 32 46 54 65 44
23 36 77 61 59 56
48 58 21 11 46
Construct a stem-and-leaf plot of the data.
Activity 3:
A sample of 29 factory workers were asked as to how long does it take each to travel from home to work on average. The following table provides their answers in minutes.
50 30 73 79 5 9
42 10 15 35 51 68
69 32 46 54 65 44
23 36 77 61 59 56
48 58 21 11 46
Produce a frequency distribution table of the data using “0 to less than 10” as the first class.
Activity 4:
A sample of 29 factory workers were asked as to how long does it take each to travel from home to work on average. The following table provides their answers in minutes.
50 30 73 79 5 9
42 10 15 35 51 68
69 32 46 54 65 44
23 36 77 61 59 56
48 58 21 11 46
Draw a histogram using “0 to less than 10” as the first class.
Review Problem 2.9
RP2.9: In a medium-sized New Zealand city, 90 houses are for sale, each having about 180 m2 of floor space. The asking prices vary. The frequency distribution shown contains the price categories for the 90 houses. Construct a frequency polygon, ogive from these data.
Practice Problem 2.16
PP2.16: Is the total sales revenue related to the advertising dollars spent by a company? The following data represent the advertising dollars and the sales revenues for various companies in a given industry during a recent year. Construct a scatter plot of the data from the two variables and discuss the relationship between the two variables.
Advertising
($ million) Sales
($ million)
4.2 155.7
1.6 87.3
6.3 135.6
2.7 99
10.4 168.2
7.1 136.9
5.5 101.4
8.3 158.2
Practice Problem 2.11
PP2.11: The table below shows Department of Foreign Affairs and Trade data for the value (in A$ million) for the top 10 import sources. Produce a bar chart for these data. On the basis of the charts for this and the previous problem, comment on Australia’s major business partners.
Import market |
A$ million |
China |
49329 |
USA |
39181 |
Japan |
21221 |
Singapore |
17878 |
Thailand |
13832 |
Germany |
13099 |
UK |
12044 |
Malaysia |
10944 |
South Korea |
10813 |
New Zealand |
10532 |
Practice Problem 2.10
PP2.11: The table below shows Department of Foreign Affairs and Trade data for the value (in A$ million) of Australian exports to the top 10 buyers of Australian goods. Construct a pie chart to represent these data. Label the slices with the corresponding percentages and give the chart an appropriate title. Comment on the effectiveness of using a pie chart to display these data.
Export market |
A$ million |
China |
94655 |
Japan |
47501 |
South Korea |
19610 |
USA |
9580 |
India |
9517 |
New Zealand |
7399 |
Singapore |
5659 |
Taiwan |
7356 |
UK |
3859 |
Malaysia |
5561 |
Activity 6:
In order to improve the customer satisfaction rating, the owner of a restaurant reviews the customer feedback forms received in past one year and summarises the type of complaints and the number of complaints received as given below:
Cost |
Percentage (%) |
Long waiting time |
9 |
Food too salty |
6 |
Overpriced |
26 |
Small portions |
21 |
Food not fresh |
16 |
No atmosphere |
12 |
Unfriendly staff |
7 |
Other |
3 |
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