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SecTIoN 1c Displaying Quantitative Data with Graphs 25

EXAMPLE Quiz scores and die rolls Skill 2.A
Describing shape

PROBLEM: The dotplots display two different sets of quantitative data. Graph (a) shows

the scores on a 20-point quiz for each of the 30 students in a statistics class. Graph (b) malerapaso/Getty Images
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shows the results of 100 rolls of a six-sided die. Describe the shape of each distribution.
(a) (b)

13 14 15 16 17 18 19 20
Quiz score
1 2 3 4 5 6
SOLUTION: Roll

(a) The distribution of statistics quiz scores is skewed to the left, with a single peak at 20 (a perfect score).

(b) The distribution of die rolls is roughly symmetric. It has no clear peak.
FoR PRAcTIce, TRY eXeRcISe 7

We can describe the shape of the distribution in part (b) of the example as approxi-
mately uniform because the frequencies are about the same for all possible rolls.

DEFINITION Approximately uniform
A distribution in which the frequency (relative frequency) of each possible value is
about the same is approximately uniform.

Some people refer to graphs with a single peak, like the dotplot of quiz scores
in part (a) of the example, as unimodal Figure 1.3 is a dotplot of the duration
.

(in minutes) of 263 eruptions of the Old Faithful geyser in July 1995, when the
Starnes family made its first trip to Yellowstone National Park. We describe this
graph as bimodal because it has two clear peaks: one at about 2 minutes and one

at about 4.5 minutes. Although we could continue the pattern with “trimodal” for
three peaks, and so on, it’s more common to refer to distributions with more than
two clear peaks as multimodal . When you examine a graph of quantitative data,
describe any pattern you see as clearly as you can.

FIGURE 1.3 Dotplot displaying the
duration (in minutes) of 263 erup-
tions of the Old Faithful geyser in
July 1995. This distribution has two
main clusters of data and two clear
peaks — one near 2 minutes and the
other near 4.5 minutes.

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Duration (min)

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