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SecTIoN 1A Statistics: The Language of Variation 5

State Birth month Age (years) Handed Height (cm) Home occupants Allergies Preferred communication
WI 11 17 Right 175 4 Yes Internet chat/IM
IN 6 16 Right 175.5 5 No In person
NY 6 17 Right 157 5 Yes In person
NC 6 17 Right 169 3 No Internet chat/IM
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MA 6 18 Right 169 3 Yes Phone call
MO 10 18 Right 170 5 No Text messaging
PA 5 14 Right 170 6 No Text messaging
IA 1 17 Left 176 2 No Text messaging
NC 5 17 Right 175 5 No Social media
CA 2 17 Right 158 8 Yes Social media
... ... ... ... ... ... ... ...
(a) Identify the individuals and variables in this data set.
(b) Classify each variable as categorical or quantitative.

SOLUTION:
(a) Individuals: 50 randomly selected U.S. high school students We’ll see in Unit 3 why choosing at random,
who completed the Census at School survey. Variables: State, as we did in this example, is a good idea.
birth month, age (years), handedness, height (cm), number of
home occupants, whether the student has allergies, preferred
communication method.
(b) Categorical: State, birth month, handedness, whether the stu-
dent has allergies, preferred communication method. Quantita- Note that birth month is categorical, even
though the values listed are numbers.
tive: Age (years), height (cm), and number of home occupants.
FoR PRAcTIce, TRY eXeRcISe 1

The proper method of data analysis depends on whether a variable is categorical
AP® EXAM TIP
or quantitative. For that reason, it is important to distinguish these two types of vari-
If you learn to distinguish ables. Be sure to include any units of measurement for a quantitative variable (like
categorical from quantita- centimeters for height). To make life simpler, we sometimes refer to categorical data
tive variables now, it will or quantitative data instead of identifying the variable as categorical or quantitative.
pay big rewards later. You
will be expected to analyze Summarizing Data with Tables
categorical and quantitative
data appropriately on the AP® A variable generally takes values that vary from one individual to another. That’s
Statistics exam. why we call it a variable! The distribution of a variable describes the pattern of
variation of the values.

DEFINITION Distribution
The distribution of a variable tells us what values the variable takes and how often
it takes each value.

We can summarize a variable’s distribution with a frequency table or a relative
frequency table. To make either kind of table, start by tallying the number of
times that the variable takes each value.

DEFINITION Frequency table, Relative frequency table
A frequency table shows the number of individuals having each value.
A relative frequency table shows the proportion or percentage of individuals having
each value.

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