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22 UNIT 1 Exploring One-Variable Data

For a discrete variable, countable means that we can number the possible
values of the quantitative variable using whole numbers. As an example, the
number of lottery tickets a person buys until they win the jackpot can take
any of the values 1, 2, 3, and so on.

Displaying Quantitative Data: Dotplots

In April 2014, managers for the city of Flint, Michigan, decided to save money
by using water from the Flint River rather than continuing to buy water sourced
from Lake Huron. Soon after, Flint residents noticed that the water coming out
of their taps looked, tasted, and smelled bad. Some residents developed rashes,
hair loss, and itchy skin. Authorities insisted that drinking water from the Flint
River was safe.
As part of its regular testing program, city officials measured lead levels in
water samples collected from 71 randomly selected Flint dwellings between
29
January and June 2015. Here are the data (in parts per billion, ppb). The
U.S. Environmental Protection Agency (EPA) requires action if a water system’s
lead level exceeds 15 parts per billion.

0 0 0 0 0 0 0 0 0 0 0 0
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0
2
2
2
2
1
1
2
2
2
1
1
3
2
3
3
2
3
2
3
3
3
2
3
5
4
5
5
5
5
5
5
4
3
3
3
6
9
7
10
8
8
7
5
7
6
6
6
18
11
20
21
13
10
Figure 1.2 is a dotplot of these data. 22 29 42 42 104
0 10 20 30 40 50 60 70 80 90 100 110
Lead level (ppb)
FIGURE 1.2 Dotplot of lead levels in water samples from 71 randomly selected Flint,
Michigan, dwellings in January to June, 2015.
DEFINITION Dotplot
A dotplot shows each data value as a dot above its location on a number line.
A dotplot is the simplest graph for displaying the distribution of a quantita-
tive variable. It is fairly easy to make a dotplot by hand for small sets of quanti-
tative data.
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