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SecTIoN 1B Displaying and Describing Categorical Data 15

their height. When all bars have the same width, the area (width × height) varies

in proportion to the height, and our eyes receive the right impression about the
quantities being compared.

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EXAMPLE Who buys iMacs? Skill 2.A
Misleading graphs

PROBLEM: When Apple, Inc., first introduced the iMac in 1998, the company wanted to know whether
this new computer was expanding its market share. (The iMac has enjoyed great success ever since!) Was
the iMac mainly being bought by previous Macintosh owners, or was it being purchased by first-time com-
puter buyers and by previous PC users who were switching over? To find out, Apple hired a firm to conduct
a survey of 500 randomly selected iMac customers. The firm categorized each customer as a new computer
purchaser, a previous PC owner, or a previous Macintosh owner. The table summarizes the survey data. 12

Previous ownership Count Percentage (%)
None 85 17.0
PC 60 12.0
Macintosh 355 71.0
Total 500 100.0

(a) A graph of the data that uses pictures instead of the more traditional bars is shown in figure (a).
How is this pictograph misleading?
(b) A bar graph of the data is shown in figure (b). Explain why this graph could be considered deceptive.

400 80
70
300
Number of buyers 200 Percent 50
60

40
30
100
20
10
None PC Macintosh None PC Macintosh
Previous computer Previous computer
(a) (b)
SOLUTION:

(a) The pictograph is misleading because the areas of the comput-
ers make it look like the number of iMac buyers who are former In part (a), the heights of the images are
Mac owners (355) is at least 10 times as large as the number correct. But the areas of the images are
misleading. The Macintosh image is about
of buyers in either of the other two categories (None: 85, PC 6 times as tall as the PC image, but its
owner: 60), which isn’t true. area is about 36 times as large!

( b) The bar graph is misleading because starting the vertical scale

at 10 instead of 0 makes it look like the percentage of iMac
buyers who previously owned a PC (12.0%) is less than half the
percentage who are first-time computer buyers (17.0%), which isn’t true.
FoR PRAcTIce, TRY eXeRcISe 11

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