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**CHAPTER 3: GRAPHICAL DESCRIPTIVE TECHNIQUES II**
**SHORT ANSWER**
1. For what type of data is a histogram appropriate?
2. Twenty-five voters participating in a recent election exit poll in Alabama were asked to state their
political party affiliation. Coding the data 1 for Republican, 2 for Democrat, and 3 for Independent, the

data collected were as follows: 3, 1, 2, 3, 1, 3, 3, 2, 1, 3, 3, 2, 1, 1, 3, 2, 3, 1, 3, 2, 3, 2, 1, 1, 3, 1, 2, 2,

1, and 3. Develop a frequency distribution and a relative frequency distribution for this data. What

does the data suggest about the strength of the political parties in Alabama?

NARRBEGIN: TeachersAges

**Teachers Ages **

The ages (in years) of a sample of 25 teachers are as follows:

47

3. {Teachers Ages Narrative} Draw a frequency histogram of this data which contains four classes. What
4. {Teachers Ages Narrative} Draw a frequency histogram of this data which contains six classes. What
5. {Teachers Ages Narrative} Draw a stem-and-leaf display of this data. What is the minimum and
maximum age of the teachers in this data set?
6. {Teachers Ages Narrative} Construct an ogive for this data. Estimate the proportion of salespersons
that are: 1) under 30 years of age; 2) 40 years of age or over; and 3) between 40 and 50 years of age.

NARRBEGIN: Test scores

**Test scores **

The scores on a calculus test for a random sample of 40 students are as follows:

63

7. {Test Grades Narrative} Construct a stem-and-leaf display for this data set. Describe the shape of the
8. {Test Grades Narrative} Construct frequency and relative frequency distributions for this data set
using seven class intervals. Describe the shape of the data set.
9. {Test Grade Narrative} Construct a relative frequency histogram for this data set and discuss its shape.
10. {Test Grades Narrative} Describe the distribution of exam scores.
11. {Test Grades Narrative} Construct a cumulative frequency and a cumulative relative frequency
distribution for this data. What proportion of the exam scores are less than 60? What proportion of the exam scores are 70 or more?
12. {Test Grades Narrative) Construct an ogive for this data set. Use the ogive to estimate the proportion
of exam scores that are between 80 and 90.
13. Forty truck buyers were asked to indicate the car dealer they believed offered the best overall service.
The four choices were A, B, C, and D as shown below: A
Construct a table showing the frequencies and relative frequencies for this data set. What proportion of car buyers rated dealer D as the best?
14. A supermarket's monthly sales (in thousands of dollars) for the last year were as follows:
Construct a relative frequency bar chart for this data set. How many observations are there in this data set?
15. Consider the following cumulative frequency distribution.
Fill in the frequencies for each class in the above table.
16. The weights of a sample of 25 workers are given (in pounds): 164, 148, 137, 157, 173, 156, 177, 172,
169, 165, 145, 168, 163, 162, 174, 152, 156, 168, 154, 151, 174, 146, 134, 140, and 171. Construct an

ogive for the data. What proportion of the worker's weights are between 160 and 180 pounds; below

150 pounds; and at or above 140 pounds, respectively?

NARRBEGIN: Insurance Company

**Insurance Company **

A representative from a local insurance agency selected a random sample of insured homeowners and recorded the number of claims made in the last three years, with the following results:
17. {Insurance Company Narrative} How many homeowners are represented in the sample?
18. {Insurance Company Narrative} How many total claims are represented in the sample?
19. {Insurance Company Narrative} What proportion of homeowners had no claims in the last three
20. {Insurance Company Narrative} What number of claims was made by the highest proportion of
homeowners?

NARRBEGIN: Electronics Company

**Electronics Company **

At a meeting of regional offices managers of a national electronics company, a survey was taken to

determine the number of employees the regional managers supervise in the operation of their

departments. The results of the survey are shown below.

21. {Electronics Company Narrative} How many regional offices are represented in the survey results?
22. {Electronics Company Narrative} Across all of the regional offices, how many total employees were
supervised by those surveyed? ANS: (1 7) + (2 11) + (3 14) + (4 8) = (5 10) = 153 PTS: 1
23. {Electronics Company Narrative} What proportion of managers supervise 3 employees?
24. {Electronics Company Narrative} What is the cumulative relative frequency corresponding to 5
employees?

NARRBEGIN: Internet Classes

**Internet Classes **

A survey of 25 students was conducted to determine how they rate the quality of Internet classes.

Students were asked to rate the overall quality from 0 (no quality at all) to 100 (extremely good

quality). The stem-and-leaf display of the data is shown below.

25. {Internet Classes Narrative} What percentage of the students rated the overall quality of Internet
26. {Internet Classes Narrative} What percentage of the students rated the overall quality of Internet
27. {Internet Classes Narrative} What percentage of the students rated the overall quality of on-line
classes as being between 50 and 75, inclusive?
28. {Internet Classes Narrative} What percentage of the students rated the overall quality of on-line
29. Explain the difference between a histogram and a line chart.
30. Briefly discuss the difference between cross-sectional data and time-series data.
31. Beef prices throughout the year (month 1 = January) are shown in the line chart below (per pound).
Describe beef prices for this given year using this line chart.
32. An economics professor wants to study the relationship between income and education. A sample of
10 individuals is selected at random, and their income (in thousands of dollars) and education (in years) are shown below: Education
Draw a scatter diagram for these data with the income on the vertical axis.
Describe the relationship between income and education.
33. The number of houses sold in Miami Springs and the average monthly mortgage rates for 18 months
randomly selected between January 2011 and April 2013 are shown in the following table.
Draw a scatter diagram with the number of houses sold on the vertical axis.
Describe the relationship between mortgage rate and number of houses sold.
34. Briefly explain the difference between correlation and causation in terms of a relationship between

*X*
35. It is speculated that the number of police officers has a negative linear relationship with number of
36. What are the two most important characteristics to look for in a scatter diagram?
37. Can a scatter diagram be used to explore the relationship between two nominal variables? Explain why
36. In its 2000 report, a company presented the following data regarding its sales (in millions of dollars),
and net income (in millions of dollars). Year
The bar chart below was used to present these data.

Assume that you are an unscrupulous statistician and want to make the data appear more positive than

they really are. Redraw the graph by being selective about which years to include, getting the desired

effect.

NARRBEGIN: Admission to ER

**Admission to ER **

The following bar chart shows the type of aspirin (if any) given to 100 cardiac patients within 15

minutes of their admission to the emergency room.

37. {Admission to ER Narrative} Notice that the

*Y*-axis of the bar chart does not start at a frequency of
zero. Create a new bar chart of the displayed data that accurately displays the frequency for each aspirin type.
38. {Admission to ER Narrative} In what way does the original bar chart distort the data as compared to a
bar chart that starts at zero on the

*Y*-axis (frequency axis)?

NARRBEGIN: Credit Hours

**Credit Hours **

The College of Business at The State University of California produced 3,400 credit hours during

Spring Semester, 2011he number and percentage of credit hours produced by each of the four

departments in the College of Business is shown below.

The following three-dimensional pie chart was constructed from the table above.
39. {Credit Hours Narrative} Construct a two-dimensional pie chart showing the percentages of credit
40. {Credit Hours Narrative} In what way does the original three-dimensional pie chart distort the data,
compared to a two-dimensional pie chart?
41. Briefly explain why the histogram below is misleading.

42. Samantha recorded her amount of exercise time (in minutes) for 100 days. Both of the line charts
below were created based on her same data set. Which line chart makes her exercise times look more variable and why?

NARRBEGIN: Home Care

**Home Care** Data are collected on the number of house calls (

*x*) made in a given week by each of 60 nurses in a

certain hospital. The same data set is displayed in each of the three histograms below.

43. {Home Care Narrative} How many nurses are there in this hospital?
44. {Home Care Narrative} Which histogram makes the differences in the house calls appear to be the
45. {Home Care Narrative} Which histogram makes the differences in the house calls appear to be the
46. {Home Care Narrative}Which graph do you think is the most appropriate display? Justify your
47. Below are two line charts where the percentage return for a stock is shown over time. The two graphs

Explain why these two line charts look different.
48. An online dating service has a quick poll on its website showing the following results. Critique the
graph portion of the table. How can it be improved?

Source: http://elearning2.utcc.ac.th/officialtcu/ECONTENT/SC123/SC123-Quiz/Quiz--Chapter%2003%20Graphical%20Descriptive%20Techniques%202%20SE.pdf

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