Conditional Relative Frequency: How to Find Them

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.”

two way table
Two way table showing movie preferences.


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?
conditional relative frequency

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.

conditional relative frequency 2

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.
crf 3

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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