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34 UNIT 1 Exploring One-Variable Data

State Percentage State Percentage State Percentage
Nevada 19.8 Oklahoma 6.1 Utah 8.6
New Hampshire 6.4 Oregon 9.7 Vermont 4.7
New Jersey 23.4 Pennsylvania 7.0 Virginia 12.7
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New Mexico 9.6 Rhode Island 13.7 Washington 14.9
New York 22.4 South Carolina 5.6 West Virginia 1.6
North Carolina 8.4 South Dakota 4.1 Wisconsin 5.1
North Dakota 4.1 Tennessee 5.5 Wyoming 3.1
Ohio 4.8 Texas 17.1
(a) Make a frequency histogram to display the data.
(b) What proportion of states have less than 10% foreign-born residents?

SOLUTION:
(a) Interval Frequency
0 to < 5 13 To make the histogram:
5 to < 10 20 1. Choose equal-width intervals that span the data. The data vary from
10 to < 15 8 1.6% to 26.7%. We choose intervals of width 5, beginning at 0: 0 to < 5,
5 to < 10, and so on. This choice results in more than the minimum of
15 to < 20 5 five intervals.
20 to < 25 3 2. Make a table. Record the number of states in each interval when making
25 to < 30 1 a frequency histogram.
3. Draw and label the axes.
4. Scale the axes. The scale on the horizontal axis matches the intervals we
20 chose in Step 1. The highest frequency in an interval is 20, so we scale the
vertical axis from 0 to 20, placing tick marks every 5 units.
15 5. Draw bars.
Frequency 10

5
0
0 5 10 15 20 25 30
Percent foreign-born residents

(b) (13 + 20)/50 = 33/50 = 0.66 of states have less than 10% foreign-born residents.

FoR PRAcTIce, TRY eXeRcISe 25

From the histogram, we can see that the distribution of the percentage of
foreign-born residents in the 50 U.S. states is skewed to the right. The graph does
not show any obvious outliers. How should we describe the center and variability
of the distribution? Because a histogram does not show individual data values,
we can only give estimates of the center and variability using the intervals on the
graph. With 50 data values, the middle value (median) falls between the 25th
and 26th values in the ordered data set, so the median percentage of foreign-born
residents is in the 5% to < 10% interval. The data vary from at least 0% to at most
29.9% foreign-born residents. Using the raw data from the example, we can con-
firm that the median is 7.3% and that the data vary from 1.6% to 26.7%.
Figure 1.8 shows two different histograms of the foreign-born resident data.
The one on the left (a) uses the intervals of width 5 from the example. The dis-
tribution has a single peak in the 5 to <10 interval. The one on the right (b) uses

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