Joint Frequency

Two Way Tables > Joint Frequency

What is Joint Frequency?

A joint frequency is how many times a combination of two conditions happens together. For example:

  • Pet owners (condition 1) who are women (condition 2),
  • Democrats (condition 1) who are married (condition 2),
  • Astronauts (condition 1) who are allergic to peanuts (condition 2),
  • Lottery winners (condition 1) who go bankrupt (condition 2),
  • Hurricanes (condition 1) that are category 5 (condition 2).

This kind of data is called bivariate data (data that has two inputs or variables). So it’s sometimes called bivariate joint frequency.

Bivariate Data in Tables

“Joint: a place where two things or parts are joined” ~ Miriam Webster.

Bivariate joint frequencies are displayed in the center of a frequency distribution table.

Joint frequency
Joint frequencies highlighted in a frequency table.

It’s called a “joint” frequency because you’re looking at where two variables join. For example, the table above shows how many people (women and men) own which pets. The value at the “joint” of women cats is 5. Therefore, the joint frequency of women who own cats is 5. The edges, or totals of the table are called marginal distributions (i.e. they appear in the margins).

What is Joint Relative Frequency?

Joint relative frequency is the ratio of the frequency in a certain category and the total number of data points in that category. In the above table, 7 people own cats, and two of those are men. So the joint relative frequency of male cat owners is 2/7. Other information you can get from the table includes:

  • Fish owners who are men is 4/7,
  • Cat owners who are women is 5/7,
  • Dog owners who are men is 6/8 = 1/4,

All of the above information was obtained by looking down the relevant column.

"Cat owners" column.
“Cat owners” column.

But you can also get similar information on joint relative frequencies by looking across rows. For example, the first row shows totals for men, so:

  • 4 out of 12 (33%) men own fish,
  • 2 out of 12 (17%) men own cats,
  • 6 out of 12 (50%) men own dogs.


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