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66 UNIT 1 Exploring One-Variable Data

We have labeled the first quartile, the median, and the third quartile and marked
them with orange line segments. The process of testing for outliers with the 1.5 ×

IQR rule is illustrated above the dotplot. Because the values of 20.9 and 31.4 are
outliers, we mark these separately. To get the finished boxplot in Figure 1.12(b)
,

we make a box spanning from Q to Q and then draw whiskers to the smallest
3
1
and largest data values that are not outliers.
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As you can see, it is fairly easy to make a boxplot by hand for small sets of quan-
titative data. Here’s a summary of the steps.
HOW TO MAKE A BOXPLOT
1. Find the five-number summary for the distribution.

2. Identify outliers using the 1.5 × IQR rule.
3. Draw and label the axis. Draw a horizontal axis and put the name of
the quantitative variable underneath it, including units if applicable.
4. Scale the axis. Look at the minimum and maximum values in the data
set. Start the horizontal axis at a convenient number less than or equal
to the minimum and place tick marks at equal intervals until you equal
or exceed the maximum.

5. Draw a box that spans from the first quartile ( Q ) to the third quartile

1
( Q ).

3
6. Mark the median with a vertical line segment that’s the same height as
the box.
7. Mark any outliers with a special symbol such as an asterisk (*).

8. Draw whiskers — lines that extend from the ends of the box to the
smallest and largest data values that are not outliers.

We can see from the boxplot in Figure 1.12 that the middle 50% of LeBron
James’s season scoring averages fall between 26.55 and 27.95 points per game.

EXAMPLE How big are the large fries? Skills 2.A, 2.B
Displaying summary statistics: Boxplots

PROBLEM: According to nutrition information provided by Burger King, the serving

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size for its large french fries is 173 grams. Two young researchers wondered if the
company is exaggerating the serving size. To find out, they went to several Burger King
restaurants in their area and ordered a total of 15 large fries. The weights of the 15
orders (in grams) are shown here. 72
178 176 173 172 179 165 179 181 186 184 181 180 183 183 187
(a) Make a boxplot to display the data. Michael Neelon/Alamy Stock Photo

(b) Does the graph in part (a) support the researchers’ suspicion that Burger King is
exaggerating the serving size of its large fries? Explain your reasoning.

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