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SecTIoN 1c Displaying Quantitative Data with Graphs 37

Using the same data, we produced the histograms in Figure 1.9(b) . By using rel-
ative frequencies, this figure makes a valid comparison of word lengths in the two
samples. The moral of the story: use relative frequencies (percentages or propor-
caution
tions) when comparing distributions, especially if the groups have different sizes.

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Journal Magazine Journal Magazine
90 30
80
25
70 20
Frequency 50 Percent 15
60
40
30 10
20
5
10
0 0
0 2 4 6 8 10 12 14 0 2 4 6 8 101214 0 2 4 6 8 10 12 14 0 2 4 6 8 101214
(a) Word length Word length (b) Word length Word length

FIGURE 1.9 Two sets of histograms comparing word lengths in articles from a biology journal and from an airline magazine.

In graph (a), the vertical scale uses frequencies. Graph (b) fixes the problem of different sample sizes by using percentages
(relative frequencies) on the vertical scale.

CHECK YOUR
UNDERSTANDING

When getting married, some people choose to buy an engagement ring for their
partner. How much do people spend on engagement rings, on average? To find out,
The New York Times and Morning Consult surveyed a random sample of 1640 U.S.
adults who bought an engagement ring. Here is a histogram of the data: 39

250

200

Number of people 150

100

50

0
0 2 4 6 8 10 12 14 16
Cost of engagement ring ($1000s)

1. About what percentage of people reported spending at least $2000 on an engage-
ment ring? Show your method clearly.
2. Describe the shape of the distribution.

3. Estimate the center and variability of the distribution.

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