Probability > Conditional Relative Frequency

You might find it helpful to read this article first: What is a two way table?

## What is Conditional Relative Frequency?

In a contingency table (sometimes called a two way frequency table or crosstabs), conditional relative frequency is it’s a fraction that tells you how many members of of a group have a particular characteristic. More technically, it is the ratio of a frequency in the center of the table to the frequency’s row total or column total.

A two way frequency table is a special type of frequency table that shows relationships between two categories. For example, the following table shows the relationships between the categories “sex” and “type of movies preferred.”

## Example

**Question**: The following contingency table shows the likelihood a person in a certain type of accommodation owns a pet. What is the conditional relative frequency for owning a pet, given that the person lives in a house?

**Solution**: The person of interest lives in a house, so use the figures from that column.

- The intersection of “House” and “Yes” is 2. This means that two people who live in a house own pets.
- The total number of people who live in houses is 18.

That gives us a conditional relative frequency of:

People who live in houses who own pets / Total number of people who live in houses = 2/18 = **1/9.**

## Example 2

**Question**: What is the probability that a pet owner lives in an apartment?

**Solution:** This time, we’re looking at the “yes” row for pets.

The number of people who live in an apartment and own a pet is 4. The total number of people who own pets is 9. That gives us: **4/9.**

Other two-way table articles you might find useful:

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**Stephanie Glen**. "Conditional Relative Frequency: How to Find Them" From

**StatisticsHowTo.com**: Elementary Statistics for the rest of us! https://www.statisticshowto.com/conditional-relative-frequency/

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