This chapter is from the book
This chapter is from the book
This chapter is from the book
Test Yourself
Short Answers
Which of the following graphical presentations is not appropriate for categorical data?
Pareto chart
scatter plot
bar chart
pie chart
Which of the following graphical presentations is not appropriate for numerical data?
histogram
pie chart
time-series plot
scatter plot
A type of histogram in which the categories are plotted in the descending rank order of the magnitude of their frequencies is called a:
bar chart
pie chart
scatter plot
Pareto chart
Which of the following would best show that the total of all the categories sums to 100%?
pie chart
histogram
scatter plot
time-series plot
The basic principle behind the ________ is the capability to separate the vital few categories from the trivial many categories.
scatter plot
bar chart
Pareto chart
pie chart
When studying the simultaneous responses to two categorical variables, you should construct a:
histogram
pie chart
scatter plot
cross-classification table
In a cross-classification table, the number of rows and columns:
must always be the same
must always be two
must add to 100%
None of the above.
Answer True or False:
Histograms are used for numerical data, whereas bar charts are suitable for categorical data.
A website monitors customer complaints and organizes these complaints into six distinct categories. Over the past year, the company has received 534 complaints. One possible graphical method for representing these data is a Pareto chart.
A website monitors customer complaints and organizes these complaints into six distinct categories. Over the past year, the company has received 534 complaints. One possible graphical method for representing these data is a scatter plot.
A social media website collected information on the age of its customers. The youngest customer was 5, and the oldest was 96. To study the distribution of the age of its customers, the company should use a pie chart.
A social media website collected information on the age of its customers. The youngest customer was 5, and the oldest was 96. To study the distribution of the age of its customers, the company can use a histogram.
A website wants to collect information on the daily number of visitors. To study the daily number of visitors, it can use a pie chart.
A website wants to collect information on the daily number of visitors. To study the daily number of visitors, it can use a time-series plot.
A professor wants to study the relationship between the number of hours a student studied for an exam and the exam score achieved. The professor can use a time-series plot.
A professor wants to study the relationship between the number of hours a student studied for an exam and the exam score achieved. The professor can use a bar chart.
A professor wants to study the relationship between the number of hours a student studied for an exam and the exam score achieved. The professor can use a scatter plot.
If you wanted to compare the percentage of items that are in a particular category as compared to other categories, you should use a pie chart, not a bar chart.
Fill in the Blank:
To evaluate two categorical variables at the same time, a _______ should be developed.
A _______ is a vertical bar chart in which the rectangular bars are constructed at the boundaries of each class interval.
A _______ chart should be used when you are primarily concerned with the percentage of the total that is in each category.
A _______ chart should be used when you are primarily concerned with comparing the percentages in different categories.
A _______ should be used when you are studying a pattern between two numerical variables.
A _______ should be used to study the distribution of a numerical variable.
You have measured your pulse rate daily for 30 days. A _______ plot should be used to study the pulse rate for the 30 days.
You have collected data from your friends concerning their favorite soft drink. You should use a _______ chart to study the favorite soft drink of your friends.
You have collected data from your friends concerning the time it takes to get ready to leave their house in the morning. You should use a _______ to study this variable.
Answers to Test Yourself Short Answers
b
b
d
a
c
d
d
True
True
False
False
True
False
True
False
False
True
False
two-way table
histogram
pie chart
bar chart
scatter plot
histogram
time-series plot
bar chart, pie chart, or Pareto chart
histogram
Problems
A Pew Research Center survey studied the key issues for employed adults who have been working at home some or all of the time. The following three summary tables present the results of that survey.
Feeling Motivated to Do Their Work
Percentage
Very Difficult
7%
Somewhat Difficult
29%
Somewhat Easy
31%
Easy
34%
Doing Work Without Interruptions
Percentage
Very Difficult
8%
Somewhat Difficult
24%
Somewhat Easy
37%
Easy
31%
Having an Adequate Workspace
Percentage
Very Difficult
4%
Somewhat Difficult
19%
Somewhat Easy
31%
Easy
47%
For each table
Construct a bar chart and a pie or doughnut chart.
Which graphical method do you think best presents these data?
What conclusions can you reach concerning how employed adults who have been working at home some or all of the time feel about being motivated to do their work?
What conclusions can you reach concerning how employed adults who have been working at home some or all of the time feel about doing work without interruptions?
What conclusions can you reach concerning how employed adults who have been working at home some or all of the time feel about having an adequate workspace?
What differences in the responses among the three issues exist?
Market researchers for a telecommunications company have summarized data collected about the payment methods customers use in the following summary table.
Payment Method
Frequency
Bank transfer (automatic)
1,212
Credit card (automatic)
1,191
Electronic check
2,243
Mailed check
871
Total
5,517
Using this table construct a bar chart and a pie or doughnut chart.
Which graphical method do you think best presents these data?
What conclusions can you reach about customer payment methods?
Medication errors are a serious problem in hospitals. The following summary table presents the root causes of pharmacy errors at a hospital during a recent time period.
Reason for Failure
Frequency
Additional instructions
16
Dose
23
Drug
14
Duplicate order entry
22
Frequency
47
Omission
21
Order not discontinued when received
12
Order not received
52
Patient
5
Route
4
Other
8
Construct a Pareto chart for these data.
Discuss the “vital few” and “trivial many” reasons for the root causes of pharmacy errors.
Students who attend a regional university located in a small town are known to favor the local independent pizza restaurant. A national chain of pizza restaurants looks to open a store in that town and conducts a survey of students who attend that university to determine pizza preferences. The following two-way table summarizes the survey variables store type and sex, based on the responses of a sample of 220 students.
Sex
Female
Male
Store Type
Local
74
71
National
19
56
Construct a two-way table that displays grand total percentages.
Construct a two-way table that displays row percentages.
Construct a two-way table that displays column percentages.
What conclusions can you reach from the tables constructed in parts (a) through (c)?
Which table do you think is most useful in reaching the conclusions in your part (d) answer?
Churning, the loss of customers to a competitor, is a problem for all companies, especially telecommunications companies. Market researchers for a telecommunications company collect data from 5,517 customers of the company. Data collected for each customer includes whether the customer churned during the last month, the sex of the customer, whether the customer is a senior citizen, and whether the customer uses paperless billing. The following three summary tables summarize these survey variables.
Churn
No
Yes
Sex
Female
1,858
883
Male
1,903
873
Churn
No
Yes
Senior Citizen
No
3,142
1,285
Yes
619
471
Churn
No
Yes
Paperless Billing
No
1,394
398
Yes
2,367
1,358
For each table
Construct a two-way table that displays grand total percentages
Construct a two-way table that displays row percentages.
Construct a two-way table that displays column percentages.
What conclusions can you reach from the tables constructed in parts (a) through (c)?
Which table do you think is most useful in reaching the conclusions in your part (d) answer?
The file Domestic Beer contains the percentage alcohol, number of calories per 12 ounces, and number of carbohydrates (in grams) per 12 ounces for 157 of the best-selling domestic beers in the United States. (Data extracted from “Find Out How Many Calories in Beer?” https://www.beer100.com/beer-calories.)
Domestic Beer
Construct a frequency distribution and a percentage distribution for percentage alcohol, number of calories per 12 ounces, and number of carbohydrates per 12 ounces (in grams).
Construct a histogram for percentage alcohol, number of calories per 12 ounces, and number of carbohydrates per 12 ounces (in grams).
Construct three scatter plots: percentage alcohol versus calories, percentage alcohol versus carbohydrates, and calories versus carbohydrates.
What conclusions can you reach about the percentage alcohol, number of calories per 12 ounces, and number of carbohydrates per 12 ounces (in grams)?
The Super Bowl Ads file contains the average ratings of 57 ads from the 2021 NFL Super Bowl broadcast. (Data extracted from T. Schad, “Rocket mortgage ads dominate Ad Meter,” USA Today, February 9, 2021, p. 4B.)
Super Bowl Ads
Construct a histogram based on these data.
What conclusions can you reach concerning Super Bowl ad ratings?
The Big Mac Starbucks file contains the cost (in U.S. $) of a McDonald’s Big Mac sandwich and a Starbucks tall latte in 11 world cities.
Big Mac Starbucks
City
Big Mac
Starbucks Tall Latte
Moscow
2.29
4.35
Johannesburg
2.53
2.18
Hong Kong
2.87
4.60
Bangkok
3.85
2.60
Dubai
4.08
4.29
Buenos Aires
4.22
2.14
London
4.32
3.58
New York
5.09
4.30
Paris
5.37
4.30
Toronto
4.38
3.15
Zurich
6.89
5.94
Source: Data extracted from “How Much a Big Mac Costs Around the World,” Business Insider, https://businessinsider.com/mcdonalds-big-mac-price-around-the-world-2018-5, and “The Starbucks Index 2019,” https://www.finder.com/starbucks.index.
Construct a scatter plot from these data.
What conclusions can you reach about the relationship between the cost of a McDonald’s Big Mac and a Starbucks tall latte in these 11 world cities?
The Potter Movies file contains the first weekend gross (in $millions) and the total domestic gross (in $millions) for the eight movies in the Harry Potter film series.
Potter Movies
Title
First Weekend
Total Domestic
Sorcerer's Stone
90.295
317.871
Chamber of Secrets
88.357
262.233
Prisoner of Azkaban
93.687
249.758
Goblet of Fire
102.335
290.201
Order of the Phoenix
77.108
292.137
Half-Blood Prince
77.836
302.089
Deathly Hallows Part I
125.017
296.132
Deathly Hallows Part II
169.189
381.193
Source: Data extracted from “Box Office History for Harry Potter Movies,” https://www.the-numbers.com/movies/franchise/Harry-Potter.
Construct a scatter plot from these data.
What conclusion can you reach about the relationship between the first weekend and total domestic grosses?
The UHDTV Wholesale Sales file contains the U.S. wholesale sales of Ultra HDTVs (in $millions) from 2013 to 2019.
UHDTV Wholesale Sales
Year
Wholesale Sales
2013
310
2014
2,238
2015
7,673
2016
12,932
2017
13,400
2018
14,300
2019
14,900
Source: Data extracted from “4K Ultra HD TVs wholesale sales revenue in the United States from 2013 to 2019,” https://www.statista.com/statistics/643511/4k-ultra-hdtv-wholesale-sales-in-us/.
Construct a time-series plot of the U.S. Ultra HDTV wholesale sales from 2013 to 2019.
What pattern does the plot reveal?
If you were asked to predict U.S. Ultra HDTV wholesale sales for 2020, what would you predict?
The MLB Salaries file contains the average MLB baseball player salaries (in $millions) for the years 2003 through 2020.
MLB Salaries
Year
Average MLB Salary
Year
Average MLB Salary
2003
2.37
2012
3.21
2004
2.31
2013
3.39
2005
2.48
2014
3.69
2006
2.70
2015
3.84
2007
2.82
2016
4.38
2008
2.93
2017
4.45
2009
3.00
2018
4.41
2010
3.01
2019
4.80
2011
3.10
2020
4.43
Source: Data extracted from https://statista.com/statistics/23621/mean-salary-of-players-in-major-league-baseball (no longer available).
Construct a time-series plot of the average MLB baseball player salaries for the years 2003 through 2020.
What pattern does the plot reveal?
If you were asked to predict the average MLB baseball player salary for 2021, what would you predict?
Answers to Test Yourself Problems
b. If you are more interested in determining which category of feeling motivated to do their job response occurs most often, then the bar chart is preferred. If you are more interested in seeing the distribution of the entire set of categories, then either the pie chart or the doughnut chart is preferred.
c. Respondents are about equally likely to feel that it is easy, somewhat easy, or somewhat difficult to feel motivated to do their job.
d. Respondents are about equally likely to feel that it is somewhat easy or somewhat difficult to do work without interruption.
e. Respondents are most likely to feel that it is easy to have adequate workspace.
f. They feel that it is easier to have adequate workspace than to feel motivated to do work or to work without interruption.
b. If you are more interested in determining which category of payment method used occurs most often, then the bar chart is preferred. If you are more interested in seeing the distribution of the entire set of categories, either the pie chart or doughnut chart is preferred.
c. Respondents are most likely to pay by electronic check and least likely to pay by mailed check.
b. The most important categories of medication errors are orders not received and frequency followed by dose, duplicate order entry, and omission.
a. through c.
Sex
Female
Male
Grand Total
Store Type
Local
33.64%
32.27%
65.91%
National
8.64%
25.45%
34.09%
Grand Total
42.28%
57.72%
100.00%
Sex
Female
Male
Grand Total
Store Type
Local
51.03%
48.97%
100.00%
National
25.33%
74.67%
100.00%
Grand Total
42.27%
57.73%
100.00%
Sex
Female
Male
Grand Total
Store Type
Local
79.57%
55.91%
65.91%
National
20.43%
44.09%
34.09%
Grand Total
100.00%
100.00%
100.00%
a. through c.
Sex and Churn
Churn
No
Yes
Grand Total
Sex
Female
33.68%
16.01%
49.69%
Male
34.49%
15.82%
50.31%
Grand Total
68.17%
31.83%
100.00%
Churn
No
Yes
Grand Total
Sex
Female
67.79%
32.21%
100.00%
Male
68.55%
31.45%
100.00%
Grand Total
68.17%
31.83%
100.00%
Churn
No
Yes
Grand Total
Sex
Female
51.21%
50.59%
49.68%
Male
48.79%
49.41%
50.32%
Grand Total
100.00%
100.00%
100.00%
d. There is very little difference between males and females in churning.
e. Row percentages are more valuable because this table compares males and females.
Senior Citizen and Churn
Churn
No
Yes
Grand Total
Senior Citizen
No
56.95%
23.29%
79.24%
Yes
11.22%
8.54%
19.76%
Grand Total
68.17%
31.83%
100.00%
Churn
No
Yes
Grand Total
Senior Citizen
No
70.97%
29.03%
100.00%
Yes
56.79%
43.21%
100.00%
Grand Total
68.17%
31.83%
100.00%
Churn
No
Yes
Grand Total
Senior Citizen
No
83.54%
73.17%
80.24%
Yes
16.46%
26.83%
19.76%
Grand Total
100.00%
100.00%
100.00%
d. Senior citizens are much less likely to churn.
e. Row percentages are more valuable because this table compares senior citizens and non-senior citizens.
Paperless Billing and Churn
Churn
No
Yes
Grand Total
Paperless Billing
No
25.27%
7.21%
32.48%
Yes
42.90%
24.61%
67.51%
Grand Total
68.17%
31.62%
100.00%
Churn
No
Yes
Grand Total
Paperless Billing
No
77.79%
22.21%
100.00%
Yes
63.54%
36.46%
100.00%
Grand Total
68.17%
31.83%
100.00%
Churn
No
Yes
Grand Total
Paperless Billing
No
37.06%
22.67%
32.48%
Yes
62.94%
77.33%
67.52%
Grand Total
100.00%
100.00%
100.00%
d. Those who use paperless billing are more likely to churn than those who do not use paperless billing.
e. Row percentages are more valuable because this table best helps to compare those with and without paperless billing.
c. The alcohol percentage is concentrated between 4% and 6%, with more between 4% and 5%. The calories are concentrated between 140 and 160. The carbohydrates are concentrated between 12 and 15. There are outliers in the percentage of alcohol in both tails. The outlier in the lower tail is due to the nonalcoholic beer O’Doul’s. The outlier in the upper tail is around 11.5%. A few beers have high calorie counts near 330 and carbohydrates as high as 32. A strong positive relationship exists between percentage of alcohol and calories and between calories and carbohydrates, and there is a moderately positive relationship between percentage alcohol and carbohydrates.
b. The ad ratings are fairly symmetrical, with many of the ad scores between 5 and 6. Very few ratings are below 4.5 or above 7.
b. There is a weak relationship between the cost of a McDonald’s Big Mac and the cost of a Starbucks tall latte in various cities.
b. There is a moderately positive relationship between the U.S. gross and the first weekend gross for Harry Potter movies.
b. Ultra HDTV sales rose dramatically from 2013 to 2016 but leveled off after that.
c. Somewhere between 15 and 16 million.
b. There has been a very strong linear increase in the salaries.
c. Because there was a decrease in 2020, the prediction is that the average salary in 2021 will be less than $5 million.