Relative frequency from a two-way table

A relative frequency is a count divided by the total. The whole question is which total — and for relative frequency the answer is always the grand total, never the row you happened to read the count from.

01 Worked Example Video

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A short walkthrough explaining what you need to know and how to solve this question type lands here once it's recorded.

02 Recognize the Question

ALEKS randomizes the numbers each attempt, but the question shape stays the same. Here are three example versions you might see.

One cell

195 adults were classified by voter registration and preferred news source.

Registered: 16 television, 17 newspapers, 33 radio, 37 internet.
Not registered: 23 television, 16 newspapers, 34 radio, 19 internet.

What is the relative frequency of adults who are registered and prefer radio? Round to two decimal places.

A whole column

Same 195 adults. Registered: 16 television, 17 newspapers, 33 radio, 37 internet.
Not registered: 23 television, 16 newspapers, 34 radio, 19 internet.

What is the relative frequency of adults who prefer the internet? Round to two decimal places.

The same cell, two questions

Same 195 adults. The not registered row is 23 television, 16 newspapers, 34 radio, 19 internet, and totals 92.

What is the relative frequency of adults who are not registered and prefer television? Round to two decimal places.

Heads up: Your ALEKS version will use different numbers. The numbers in the practice below are different too — that way you're exercising the move, not memorizing one answer.

03 The Rule

relative frequency = count ÷ grand total the denominator never changes

a cell, a row or a column can be the count whatever the question names

Relative frequency asks what share of everyone falls in a category. So the bottom of the fraction is the grand total every single time, whether the top is one cell, a whole row, or a whole column. That fixed denominator is what separates it from a conditional probability, where the denominator shrinks to the group you were told to look at.

Common slips

(1) Divided by the row total. That answers a different question — a conditional one. (2) Read the wrong cell. Two-way tables reward pointing at the square before dividing. (3) Assumed the relative frequencies of a row must sum to 1. They sum to that row’s share of the whole, not to 1.

04 Practice — Step by Step

One denominator, always

A leisure centre logged its 200 visitors one Saturday by membership status and by which facility they used.

One visit is chosen at random. Round answers to the nearest hundredth.

Step 1

A single cell

What is the relative frequency of visits that were a guest using the pool?

Step 2

A whole row

What is the relative frequency of visits made by members?

Step 3

The one that is not a relative frequency

A classmate answers the first question with 0.35. What did they compute?

Q11 Q13

Relative frequency from a two-way table

Why this is the whole question