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38 UNIT 1 Exploring One-Variable Data

SECTION 1C Summary

• There are two types of quantitative variables: discrete and continuous. A dis-
crete variable can take a countable set of possible numeric values with gaps
between them on the number line. A continuous variable can take any value
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in an interval on the number line. Discrete variables usually result from count-
ing something; continuous variables usually result from measuring something.
• You can use a dotplot, stemplot, or histogram to display the distribution of

a quantitative variable. A dotplot displays individual data values on a number
line. Stemplots separate each data value into a stem and a one-digit leaf. His-
tograms plot the frequencies (counts) or relative frequencies (proportions or
percentages) of values in equal-width intervals.

• When examining any graph of quantitative data, look for an overall pattern and
for clear departures from that pattern. Shape, center, and variability describe
the overall pattern of the distribution of a quantitative variable. Outliers are
observations that lie outside the overall pattern of a distribution.
• Some distributions have simple shapes, such as roughly symmetric, skewed to

the left, or skewed to the right. A distribution in which the frequency (relative
frequency) of each possible value is about the same is approximately uniform.

• The number of peaks is another aspect of overall shape. So are distinct
clusters and gaps. A single-peaked graph is sometimes called unimodal, and a
AP® EXAM TIP double-peaked graph is sometimes called bimodal .
AP® Daily Videos

• Dotplots, back-to-back stemplots, and histograms can also be used to compare
Review the content of this distributions of quantitative data. When comparing the distribution of a quan-
section and get extra help titative variable in two or more groups, be sure to compare shape, outliers,
by watching the AP® Daily center, and variability.
Videos for Topics 1.5 and 1.6,

which are available in AP® • Histograms are for quantitative data; bar graphs are for categorical data. In
Classroom. both types of graphs, be sure to use relative frequencies when comparing data
sets of different sizes.

1C Tech Corner

TI-Nspire and other technology instructions are on the book’s website at
bfwpub.com/tps7e.
1. Making histograms Page 35

SECTION 1C exercises

1. Protecting wood How can we help wood surfaces resist 2. Social media A social media company records data on
weathering, especially when restoring historic wooden each of its users for several variables: internet provider,
buildings? In a study that attempted to answer this age (in years), how many times they visited the site,
question, researchers prepared wooden panels and then total time spent on the site, country where they live,
exposed them to the weather. Here are some of the vari- and how long since they created a member profile.
ables the researchers recorded: type of wood, paint thick- Classify each variable as categorical, quantitative (dis-
ness, paint color, weathering time (1, 2, or 3 months), and crete), or quantitative (continuous).
number of blemishes. Classify each variable as categori-
cal, quantitative (discrete), or quantitative (continuous).

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