The joint relative frequency refers to the fraction of data that lies in a given category compared to the total population. It is obtained by taking the ratio of the joint frequency of that category and the total frequency.

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.

**How to Find a Joint Relative Frequency?**

- Given the bivariate data (data involving two categories), write down the frequencies in the form of a two-way table.
- Calculate the relative frequency for each category by dividing the frequency by the total frequency of the data.
- Replace the actual frequencies with the relative frequencies in the two-way table.
- Convert the relative frequencies to percentages for better understanding.

**Example 1**:

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

**Solution**: We are given the following pieces of information in the above table.

- There are 15 men whose eye color is black.
- There are 20 women whose eye color is black.
- There are 35 men whose eye color is blue.
- There are 30 women whose eye color is blue.

The above frequency values are called joint frequencies because we have two categories – gender and eye color. Such a table summarizing information about two different categories is called a two-way table.

Total Frequency = Total number of people = 15 + 20 + 35 + 30 = 100. Therefore we divide each of the above frequencies by the total frequency which is 100.

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 the following bivariate data about blood type and place of residence of 250 individuals given in the form of a two-way table. We represent the data by constructing a joint relative frequency table.

Urban | Rural | |

Blood Type A | 50 people | 45 people |

Blood Type B | 70 people | 25 people |

Blood Type O | 30 people | 30 people |

**Solution**: We first calculate the total frequency by adding up all the frequencies in the above table.

Total Frequency = 50 + 45 + 70 + 25 + 30 + 30 = 250.

We divide each value by the total number of individuals to find the relative joint frequency. For instance, if there are 50 people who have Blood Type A and live in an Urban area, then we calculate the joint relative frequency as follows.

Joint relative frequency = 50/250 = 1/5 = 0.20. This means that around 20% of the total population has blood type A and lives in an urban area.

We calculate the joint relative frequency table. The proportions below are given in percentages.

Urban | Rural | |

Blood Type A | 50/250= 20% | 45/250= 18% |

Blood Type B | 70/250 = 28% | 25/250= 10% |

Blood Type O | 30/250 = 12% | 30/250= 12% |

**Interpreting 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.