Sample Problems on
Bar Graph Scales

1. Employee Salaries

The following table illustrates the average employee salary at Smith, Inc. for each of the last fifteen years.

Year Salary
(in thousands)
1983 32.5
1984 33.25
1985 33.35
1986 37.4
1987 32
1988 35.8
1989 37.8
1990 34.48
1991 40
1992 39.5
1993 36.1
1994 35.4
1995 37.5
1996 38
1997 36.9

Mrs. Smith, the general manager of Smith, Inc., has been asked to submit to the local newspaper a bar graph illustrating the average employee salary in her company for each of the last 15 years. If you were Mrs. Smith, how would you create the vertical scale of the bar graph so as to maximize the appearance of increasing average salary? How would you create the bar graph so as to emphasize the company's stability? If you were an outside observer, how would you create the bar graph so as to present an accurate representation of the changing average salaries?


2. Basketball Scores

Your basketball team, the Jaguars, has been asked to create a bar graph illustrating your team's scores for each of its last ten games. The following table illustrates these scores.

Game Score
1 67
2 72
3 71
4 68
5 70
6 65
7 75
8 78
9 77
10 80

Create a bar graph of these scores for the Jaguars using a vertical scale of 0.5 points. Next, create a bar graph of the scores using a vertical scale of 5 points. In which bar graph does it appear that the Jaguars' scores are increasing the most? Why? How could you create an accurate representation of the scores from these ten games?


3. Quality Motor Company

Quality Motor Company (QMC) is claiming that their cars have increased in quality more significantly than the cars of their competitors. They plan to use bar graphs showing the average longevity of cars from each company, as well as their own, for each of the last 12 years. Given the following data for the company, how should QMC scale its bar graph so as to emphasize increase in quality? In general, how should they scale the bar graphs for their competitors (larger or smaller scale)? Is this an accurate comparison of the companies? If not, how could you create one?

Year Avg. # Years Until
Repairs are Needed
1986 2.6
1987 2.3
1988 2.5
1989 2.5
1990 2.8
1991 1.9
1992 3.0
1993 3.1
1994 2.8
1995 3.2
1996 3.6
1997 3.5

4. Mall Safety

You are the manager of the local mall, and you want to express to the public the safety of your mall. The following data has been collected during the past year:

Month # Crimes
Reported
Jan. 2
Feb. 1
Mar. 1
Apr. 3
May 4
June 5
July 5
Aug. 4
Sept. 1
Oct. 2
Nov. 1
Dec. 3

What is the best way to present this data, using a bar graph (remembering that your goal is to emphasize the mall's safety)? Possible methods of manipulating the bar graph include changing its scale and the number of months shown (i.e. show only every 3rd month, etc.).