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28 UNIT 1 Exploring One-Variable Data

comparing Distributions of Quantitative Data

Some of the most interesting statistics questions involve comparing two or more
groups. Do high school graduates earn more, on average, than students who do
not graduate from high school? Which of several popular diets leads to greater
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long-term weight loss? Just like when describing the distribution of a quantitative
variable, you should always discuss shape, outliers, center, and variability when-
ever you compare distributions of quantitative data.

EXAMPLE Household size in South Africa and the United Kingdom Skill 2.D
comparing distributions of quantitative data

PROBLEM: How do the numbers of people living in households in the

United Kingdom (U.K.) and South Africa compare? To help answer this
question, we selected separate random samples of 50 households from each
34
country. Here are dotplots of the number of people in each household.
Compare the distributions of household size for these two countries.

South Africa

FrankvandenBergh/Getty Images
Country 0 5 10 Household size 20 25 30
15

United Kingdom

0 5 10 15 20 25 30
Household size

SOLUTION: AP® EXAM TIP
Shape: The distribution of household size for the U.K. sample is roughly When comparing distribu-
symmetric, with a single peak at 4 people. The distribution of household tions of quantitative data, it’s
size for the South Africa sample is skewed to the right, with a single peak not enough just to list values
at 4 people and a clear gap between 15 and 26 people. for the center and variability
Outliers: There are no apparent outliers in the U.K. dotplot. The two of each distribution. You
largest values in the South Africa dotplot — households with 15 and have to compare these values
26 people — appear to be outliers. explicitly, using words like
Center: Household sizes for the South Africa sample tend to be larger “greater than,” “less than,” or
(median = 6 people) than for the U.K. sample (median = 4 people). “about the same as. And be

Variability: The household sizes for the South Africa sample vary more sure to include context!
(from 3 to 26 people) than for the U.K. sample (from 2 to 6 people).
FoR PRAcTIce, TRY eXeRcISe 13

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