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SecTIoN 1A Statistics: The Language of Variation 7

Note that the frequencies and relative frequencies listed in these tables are
caution
not data. The frequency and relative frequency tables summarize the data by

telling us how many, or what proportion or percentage of, students in the Census
at School sample prefer each method of communicating with friends.
The same process can be used to summarize the distribution of a quantita-
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tive variable. However, it would be hard to make a frequency table or a relative
frequency table for quantitative data that take many different values, like height
(cm) in the Census at School data set. We’ll look at a better option for summariz-
ing quantitative variables in Section 1C.
FROM DATA ANALYSIS TO INFERENCE

Sometimes we’re interested in drawing conclusions that go beyond the data at hand.
That’s the idea of statistical inference. In the Census at School survey, 12 of the 50 ran-

domly selected students prefer communicating in person with their friends. That’s 24%
.
of the sample Can we conclude that exactly 24% of the population of students who
completed the online survey prefer communicating in person with their friends? No.
If another random sample of 50 students who completed the survey were selected,
the percentage who prefer communicating in person with their friends would proba-
bly not be exactly 24%. Can we at least say that the actual population value is “close”
to 24%? As you will learn in future units, that depends on what we mean by “close.”
Our ability to do statistical inference is determined by how the data are pro-
duced. Unit 3 discusses the two main methods of collecting data — sampling and
experiments — and the types of conclusions that can be drawn from each. As the
Smelling Parkinson’s activity at the beginning of this unit illustrates, the logic
of inference rests on asking, “What are the chances?” Probability, the study of
chance behavior, is the focus of Units 4 and 5. We’ll introduce the most common
methods of statistical inference in Units 6–9.

CHECK YOUR
UNDERSTANDING

Malena is a car buff who wants to find out more about the cars that high school
students drive. The principal of a local high school gives Malena permission to go
to the student parking lot and record some data. Later, Malena does some inter-
net research on each model of car in the parking lot and makes a spreadsheet that
includes each car’s license plate, model, year, number of stickers on the car, color,
weight (in kilograms), whether it has a navigation system, and highway gas mileage.

1. Identify the individuals and variables in Malena’s study.

2. Classify each variable as categorical or quantitative.
A professor suspects that most students in an 8 A.M . introductory statistics class did
not complete the pre-class reading assignment. To find out, the professor gave the stu-
dents a 10-question pop quiz about the assigned reading at the beginning of class. Here
are the number of correct answers on the pop quiz for the 50 students in the class:
9 8 6 7 7 8 4 7 7 8 8 8 6 7 8 8 7 7 6 8 9 7 6 5 7
8 8 7 9 6 6 6 8 9 5 8 7 7 7 7 2 4 8 3 6 5 5 8 7 3
3 . Make a frequency table and a relative frequency table to summarize the distribu-

tion of number of correct answers on the pop quiz.

4. What proportion of students got fewer than 7 correct answers on the pop quiz?
Does this result support the professor’s belief that most students did not com-
plete the pre-class reading assignment? Justify your answer.

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