Resources For Teachers For Tutors For Students & Parents Pricing
Pre-Algebra Data and graphs

Two-way frequency tables

20 practice questions 0 video lessons Theory + worked examples

Two-Way Frequency Tables

Texas Pre-Algebra (TEKS) • Standard 8.5(I) • Data & Graphs

Two-Way Frequency Tables is a topic in Data & Graphs in the Texas Essential Knowledge and Skills. It is aligned to Standard 8.5(I), which requires students to construct and interpret two-way frequency tables.

A two-way frequency table organizes counts by two categories with row and column totals.

Texas Pre-Algebra (TEKS) › Data & Graphs › Two-Way Frequency Tables  —  Standard 8.5(I)

Create a free accountTrack your progress and save your work as you go.
Create free account

Theory

A two-way frequency table shows counts for two categories at once, with row and column totals.

Relative frequency is a cell divided by a total.
Two-way frequency table A two-way table shows counts by two categories with totals. Cat Dog Total Boys 8 6 14 Girls 10 6 16 Total 18 12 30
A two-way table with totals.
Two-way tables Two-way tables Two-way tables counts by two categories row and column totals relative frequency = cell ÷ total
Reading the table.

Relative frequency:

\[\text{relative frequency}=\dfrac{\text{cell}}{\text{total}}\]
relative frequency is a cell divided by a total
Totals must add up to the grand total.

How to read a two-way table

  1. Find the relevant cell.
  2. Use row/column totals as needed.
  3. Divide by a total for relative frequency.
  4. Check the totals add up.
Example 1 — Read a cell
From the table, how many boys prefer cats?
Solution

Read the Boys–Cat cell.

\(8\)
8
Example 2 — Total
How many students are there in all?
Solution

The grand total.

\(30\)
30
Example 3 — Relative frequency
What fraction of all students are girls who like dogs?
Solution

Cell over grand total.

\(\dfrac{6}{30}\)\(=\)\(0.2\)
0.2
Example 4 — Row total
How many girls are there?
Solution

The Girls row total.

\(16\)
16

Common pitfalls

Watch which total you divide by.
Totals must add up to the grand total.
Cells are counts, not percents (until divided).

Frequently asked questions

What is a two-way table?

A table of counts by two categories.

What is relative frequency?

A cell divided by a total.

What are the margins?

The row and column totals.

How many students in the example?

\(30\).