Construct and Interpret Two-Way Tables

Students organize bivariate categorical data into two-way frequency tables, calculating row totals, column totals, and the grand total. They identify patterns of association by comparing frequencies in relative terms (e.g., row percentages), deciding whether the two categorical variables are associated.

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Grade 8 · Statistics and Probability: Bivariate Data · question 1 of 3

0 of 20

20 rungs. A star at the top.

	Grade
Club	Grade 6	Grade 7
Band	30	12
Chorus	56	11

In all, how many students are in grade 6?

Your answer:

How it is taught

0:00 of 3:52

A two-way table sorts people by two questions.

Raw counts mislead when groups are different sizes.

Compare each share to its own group total.

	Age
Vote	Under 40	40 and up
Park	12	36
Pool	57	38

Read it: A two-way table

Of the 24 athletes, 18 buy lunch: 18/24 = 3/4 of the athletes. The athletes' total, 24, is at the bottom of their column.

Find the group the question is about: its row or its column.
Find that group's total: at the end of its row, or at the bottom of its column.
Divide the cell by that total. A missing cell is its row's total take away the rest of the row.

Each cell counts the members with one answer to each question, so every member is in exactly one cell.

The rows add to the totals at their ends, the columns to the totals at the bottom, and all of them to 50.

A share is always of some group, so it divides by that group's total: of the athletes, by 24.

A relative frequency is a cell ÷ the total of the group the question asks about.

Dividing by the Buys row's total: 18/30.

Of the athletes means the athletes' total, at the bottom of their column: 18/24 = 3/4.

A club has 20 members who play chess. 11 of them also play soccer. How many chess players do not play soccer? — 9. The chess players' total is 20: 20 − 11 = 9.

Pets and Music — a survey of 40 students

We asked forty students two questions: do you have a pet, and do you play music? Let's organize their answers.

A two-way table is perfect for this — pets across the top, music down the side.

Fifteen students said yes to BOTH — they have a pet AND play music.

Five play music but don't have a pet.

Add across the row: fifteen plus five is twenty music players in all.

Nine students have a pet but don't play music.

Eleven have neither — no pet and no music.

Row two total: nine plus eleven is twenty non-musicians.

Now down the columns: twenty-four pet owners, and sixteen students without a pet.

Adding either way — twenty plus twenty, or twenty-four plus sixteen — gives forty. That's our grand total.

To spot a pattern, compare the rows. Of music players, fifteen out of twenty — seventy-five percent — have pets. Of non-musicians, only nine out of twenty — forty-five percent.

Grade 8 · Organizing data and spotting an association

Seventy-five percent versus forty-five percent — a big gap! Pets and music are associated in this class.

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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