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32 UNIT 1 Exploring One-Variable Data

Here is a stemplot of the percentage of residents aged 65 and older in the 50 U.S.
states: 37

11 18
12 6
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13 9
14 23
15 44445677889999
16 23444557999 Key: 19|3 means 19.3% of
17 0112225567 the state’s residents are
18 12477 aged 65 and older.
19 39
20 56

2. The largest data value is for Maine. What percentage of Maine residents are 65
or older? (Florida has the second largest data value.)
3. Make another stemplot of the data by splitting stems. What does this new graph
reveal that is not apparent from the original stemplot?

Displaying Quantitative Data: Histograms

You can use a dotplot or a stemplot to display quantitative data. Both of these
types of graphs show every individual data value. However, for large data sets, this
can make it difficult to see the overall pattern in the graph. We often get a cleaner
picture of the distribution by grouping nearby values together. Doing so allows us
to make a new type of graph: a histogram.

DEFINITION Histogram
A histogram shows each interval as a bar. The heights of the bars show the fre-
quencies or relative frequencies of values in each interval.

Figure 1.7 shows a dotplot and a histogram of the durations (in minutes) of
263 eruptions of the Old Faithful geyser in July 1995. Notice how the histogram
groups nearby values together into equal-width intervals.

50
45
40
35
Frequency 30
25
20
15
10
5
0
1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
(a) Duration (min) (b) Duration (min)
FIGURE 1.7 (a) Dotplot and (b) histogram of the duration (in minutes) of 263 eruptions of the Old Faithful geyser in July 1995.

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