Joint Relative Frequency

A joint relative frequency refers to the fraction of data that lies in a given category compared to the total population under consideration. For example, suppose we are given data about two categories such as hair color and nationality of 500 people. Suppose there are 165 people who have brown hair and are Americans. Then the joint relative frequency for this category is 165/500 = 0.35. This means that 35% of the people have brown hair and American nationality.

Use of Joint Relative Frequency:

The advantage of knowing joint relative frequency is that we get a sense of how many people, as a percentage of the total, belong to a particular category.

The relative joint frequencies can be conveniently presented in the form of a joint relative frequency table. The joint relative frequency table is mostly used in analyzing nominal data.

How to construct a joint relative frequency table?

1. Given the bivariate data, write down the frequencies in the form of a two way table.
2. Calculate the relative frequency for each category by dividing the frequency by the total frequency of the data.
3. Replace the actual frequencies by the relative frequencies in the two way table.
4. Convert the relative frequencies to percentages for better understanding.

Example 1: Consider following bivariate data about eye color and gender, given in the form of a two-way table. Represent the data by constructing a joint relative frequency table.

Solution: We calculate the relative frequency by dividing each frequency by the total number of people which is 100 and then convert it to a percentage. The joint relative frequency table is given as,

Example 2: Consider following bivariate data about blood type and place of residence of 250 individuals, given in the form of a two-way table. Represent the data by constructing a joint relative frequency table.

Solution: We divide each value by the total number of individuals to find the relative joint frequency. The proportions below are given in percentage.