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.
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.
A two-way table with totals.
Reading the table.
Relative frequency:
\[\text{relative frequency}=\dfrac{\text{cell}}{\text{total}}\]
Totals must add up to the grand total.
How to read a two-way table
- Find the relevant cell.
- Use row/column totals as needed.
- Divide by a total for relative frequency.
- Check the totals add up.
Example 1 — Read a cell
From the table, how many boys prefer cats?
Solution
Read the Boys–Cat cell.
| \(8\) |
Example 2 — Total
How many students are there in all?
Solution
The grand total.
| \(30\) |
Example 3 — Relative frequency
What fraction of all students are girls who like dogs?
Solution
Cell over grand total.
| \(\dfrac{6}{30}\) | \(=\) | \(0.2\) |
Example 4 — Row total
How many girls are there?
Solution
The Girls row total.
| \(16\) |
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?
\(30\).
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