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SecTIoN 1c Displaying Quantitative Data with Graphs 31

COMPARING DISTRIBUTIONS WITH STEMPLOTS
You can use a back-to-back stemplot with common stems to compare the distribu-
tion of a quantitative variable in two groups. The leaves on each side are placed
in order leading out from the common stem. For example, Figure 1.6 shows a

back-to-back stemplot of the 19 middle school students’ resting pulse rates and
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their pulse rates after 5 minutes of running.

FIGURE 1.6 Back-to-back stem- Resting After exercise
plot of 19 middle school students’ 9888 6
resting pulse rates and their pulse 8664110 7
rates after 5 minutes of running. 8862 8 6788
60 9 02245899
4 10 044 Key: 8|2 is a student
11 8 whose pulse rate is
0 12 44 82 beats per minute.
13
14 6

Let’s compare the distributions. As always, we discuss shape, outliers, center,
and variability.
Shape: The distribution of resting pulse rates is skewed to the right, with a sin-
gle peak on the 70s stem. The distribution of after-exercise pulse rates is also
skewed to the right, with a single peak on the 90s stem.
Outliers: The student whose resting pulse rate was 120 bpm appears to be an
outlier in that group. The student whose after-exercise pulse rate was 146 bpm
appears to be an outlier in that group.
Center: The students’ resting pulse rates tended to be lower (median = 76 bpm)

than their after-exercise pulse rates (median = 98 bpm).

Variability: The after-exercise pulse rates vary more (from 86 bpm to 146 bpm)

than the resting pulse rates (from 68 bpm to 120 bpm).
CHECK YOUR
UNDERSTANDING

1. Which is healthier: dairy yogurt or plant-based yogurt? The Nutrition Action Health-
letter provided data on calories, saturated fat, protein, calcium, and total sugars for
36
many popular brands of yogurt. Here are parallel dotplots that compare the calo-
ries in single-serving containers of 57 brands of dairy yogurt and 26 brands of plant-
based yogurt. Describe similarities and differences in the two distributions.

Dairy
80 100 120 140 160 180 200 220 240 260 280
Calories

Plant-based
80 100 120 140 160 180 200 220 240 260 280
Calories

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