NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 13: Summarizing Bivariate Categorical Data in a Two-Way Table
Date:
2/6/15
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4. What percentage of students preferred each flavor? Round to the nearest tenth of a percent.
Answers will vary based on data gathered in Exercise 1.
Chocolate:
≈ . %
Strawberry:
≈ . %
Vanilla:
≈ %
5. Do the numbers in the chart above summarize data on a categorical variable or a numerical
variable?
The numbers in this table summarize data on a categorical variable—preferred flavor of ice
cream.
Exercises 6–8 (5 minutes)
Let students work with a partner to discuss and answer Exercises 6–8. These exercises review the concepts of random
samples and representative samples from Grade 7. You may also use these exercises to structure a class discussion.
6. Do the students in your class represent a random sample of all students in your school? Why or why not? Discuss
this with your neighbor.
No, because there is no indication that the students were selected randomly.
7. Is your class representative of all the other classes at your school? Why or why not? Discuss this with your
neighbor.
This class might be representative of the other eighth-grade classes, but might not be representative of sixth- and
seventh-grade classes.
8. Do you think the principal will get an accurate estimate of the proportion of students that prefer each ice cream
flavor for the whole school using only your class? Why or why not? Discuss this with your neighbor.
It is unlikely to give you a good estimate. It would depend on how representative your class is of all of the students
at your school.
Example 1 (3–5 minutes)
In this example, be sure that students understand the vocabulary. Univariate means one
variable. Thus, univariate categorical data means that you have data on one variable that
is categorical, such as favorite ice cream flavor. A one-way frequency table is typically
used to summarize values of univariate categorical data. When the data is categorical, it is
customary to convert the table entries to relative frequencies instead of frequencies. In
other words, you should use the fraction,
frequency
total
, which is the relative frequency or
proportion for each possible value of the categorical variable.
Point out the prefix uni -
means one. So, univariate
means one variable.
Some students may
recognize the word table,
but may not yet know the
mathematical meaning of
the term. Point out that
this lesson defines table as
a tool for organizing data.
Categorical variables are
variables that represent
categorical data. Data that
represent specific descriptions
or categories are called
categorical data.