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26 UNIT 1 Exploring One-Variable Data

Describing Distributions of Quantitative Data

Here is a general strategy for describing the distribution of a quantitative variable.

HOW TO DESCRIBE THE DISTRIBUTION OF
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A QUANTITATIVE VARIABLE

In any graph, look for the overall pattern and for clear departures from that pattern.

• You can describe the overall pattern of a distribution by its shape,

center, and variability.

• An important kind of departure is an outlier, an observation that falls
outside the overall pattern.

Variability is sometimes referred to as spread. We prefer variability because stu-
dents often think that spread refers only to the distance between the maximum
and minimum values of a quantitative data set (the range ).
We will discuss more formal ways to measure center and variability and to iden-
tify outliers in Section 1D. For now, just use the middle value in the ordered data set
(what you may have learned as the median in previous math classes) when describ-
ing center and the minimum and maximum values when describing variability.
Let’s practice with the dotplot of lead levels in water samples from 71 ran-
domly selected Flint, Michigan, dwellings that you saw in Figure 1.2 .

0 10 20 30 40 50 60 70 80 90 100 110
Lead level (ppb)
Shape: The distribution of lead level is skewed to the right, with a single peak
at 0 ppb.
Outliers: There is one obvious outlier at 104 ppb. The two lead levels of 42 ppb
may also be outliers.
Center: The middle value (median) is a lead level of 3 ppb.
Variability: The lead levels vary from 0 to 104 ppb.
When describing a distribution of quantitative data, don’t forget: S tatistical
O pinions C an V ary (Shape, Outliers, Center, Variability).

EXAMPLE eating healthy Skill 2.A
Describing distributions of quantitative data

PROBLEM: How healthy is plant-based yogurt? Here is a dotplot of data

on the amount of added sugar, in teaspoons (tsp), in single-serving con-
tainers of several plant-based yogurt brands: 32

Sara Stathas/Alamy Stock Photo

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