Back to Tutor Intake Assessment: Understand that patterns of association can also be seen in bivariate categorical data

Two-Way Tables -- Tutor Intake Assessment

This is a quick check on two-way frequency tables: reading them,
computing relative frequencies, and using them to judge whether two
categorical variables are associated. The goal is to see where to focus
our first sessions together, not to grade you. Work independently,
without notes.

Grade 8·8 problems·~12 min·Common Core Math - Grade 8·container·8-sp-a-4

Work through problems with immediate feedback

Concepts

A survey collects two pieces of information from 30 students:
whether they eat breakfast on school days (Yes/No), and whether
they feel tired by noon (Yes/No). Which display is appropriate
for looking at patterns between these two variables?

A scatter plot, since scatter plots work for any bivariate data

A two-way table, because both variables are categorical (Yes/No), not numerical

A scatter plot, plotting 'Yes' as 1 and 'No' as 0 on both axes

Neither -- categorical data cannot reveal patterns of association

In a two-way table of curfew (Yes/No) versus chores (Yes/No), a
student computes that 80% of students WITH a curfew also have
chores. The student then states: "So 80% of students WITH
chores also have a curfew." Is this second statement
necessarily true?

Yes -- if 80% goes one way, it must be 80% the other way too

No -- these are two different relative frequencies (row vs. column) with different denominators, and they are not generally equal

Yes, because both statements involve the same two categories

No -- because relative frequencies can only be computed one way, not both

Procedures

A two-way table of curfew status versus chore status for 40
students is shown below.

	Chores	No Chores	Total
Curfew	16	4	20
No Curfew	8	12	20
Total	24	16	40

How many students have BOTH a curfew AND chores (the joint
frequency for that cell)?

Using the same two-way table as above:

	Chores	No Chores	Total
Curfew	16	4	20
No Curfew	8	12	20
Total	24	16	40

What percent of students WITH a curfew also have chores (the row
relative frequency for the Curfew row, Chores column)? Enter your
answer as a whole number percent (no % sign needed).

Using the same two-way table:

	Chores	No Chores	Total
Curfew	16	4	20
No Curfew	8	12	20
Total	24	16	40

What percent of students WITH chores also have a curfew (the
column relative frequency for the Chores column, Curfew row)?
Round to the nearest whole number percent (no % sign needed).

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