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SecTIoN 1D Describing Quantitative Data with Numbers 67

SOLUTION:

(a) 165 172 173 176 178 179 179 180 181 181 183 183 184 186 187
Min Q Med Q Max
3
1
−
=
IQR =Q 3 −Q 1 = 183 176 7 1. Find the five-number summary.
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×=
−
Low outliers <Q 1 − 1.5×IQR = 176 1.57 165.5 2. Identify outliers.
×=
+
High outliers >Q 3 + 1.5×IQR = 183 1.57 193.5 3. Draw and label the axis.
4. Scale the axis.
The order of large fries that weighed 165 grams is an outlier. 5. Draw a box from Q 1 to Q 3 .
6. Mark the median.
7. Mark any outliers.
* 8. Draw whiskers.
165 170 175 180 185 190
Weight (g)

(b) No. From the boxplot, Q 1 = 176, so at least 75% of the orders of large fries that the researchers
bought from local Burger King restaurants weighed 176 grams or more. Only the outlier (165 grams)
and one other order (172 grams) of large fries weighed less than the advertised 173-gram
serving size.

FoR PRAcTIce, TRY eXeRcISe 31

Boxplots provide a quick summary of the center and variability of a distribution.
The median is displayed as a vertical line segment in the central box, the interquar-
tile range is the length of the box, and the range is the length of the entire plot,
including outliers. Note that some statistical software orients boxplots vertically.
Boxplots don’t give a complete picture of the shape of a distribution because
caution
they do not display each individual data value. From the boxplot in the example,
we can see that the distribution of weight for orders of Burger King’s large fries is
skewed to the left because the left half of the distribution varies from 165 to 180
grams, while the right half of the distribution varies from 180 to 187 grams. But we
can’t identify peaks, gaps, or clusters from a boxplot. For instance, the following
dotplot displays the duration, in minutes, of 263 eruptions of the Old Faithful gey-
ser. The distribution of eruption durations is clearly bimodal (two-peaked). How-
ever, the boxplot of the data hides this important information about shape.

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
Duration (min) Duration (min)

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