Question

Consider the rufus School activities-data shown below:

| Basketball| Chess Club| Jazz Band| Not Involved| Total
---|---|---|---|---|---
Males| $20$| $2$| $8$| $10$| $40$
Females| $20$| $10$| $10$| $20$| $60$
Total| $40$| $12$| $18$| $30$| $100$

Prepare a bivariate table with relative frequency.
Based on a bivariate table with relative frequency, what is the relative frequency of students not involved in any activity?

Answer 1

We will first create a bivariate table from the data given in the table, and then divide each value into the total number of students. Finally, we will find the frequency of students not involved in any activity.

Complete step-by-step solution:
In the given data we can see that there are total $3$ school activities in which males and females both can take part in.
Now from the table we can see that there are a total $100$ students out of which the total number of males is $40$ and the total number of females is $60$.
Now to get the frequency of the number of students in the school’s activity we have to divide the number of students which are involved in an activity by the total number of students in the table.
Same way we will find the frequency of the number of students which are not involved in any activity by dividing the total number of students not involved in any activity by the total number of students in the table.
Therefore, the frequency can be found as:

| Basketball| Chess Club| Jazz Band| Not Involved| Total
---|---|---|---|---|---
Males| $\dfrac{{20}}{{100}}$| $\dfrac{2}{{100}}$| $\dfrac{8}{{100}}$| $\dfrac{{10}}{{100}}$| $\dfrac{{40}}{{100}}$
Females| $\dfrac{{20}}{{100}}$| $\dfrac{{10}}{{100}}$| $\dfrac{{10}}{{100}}$| $\dfrac{{20}}{{100}}$| $\dfrac{{60}}{{100}}$
Total| $\dfrac{{40}}{{100}}$| $\dfrac{{12}}{{100}}$| $\dfrac{{18}}{{100}}$| $\dfrac{{30}}{{100}}$| $\dfrac{{100}}{{100}}$

On simplifying the frequencies, we get:

| Basketball| Chess Club| Jazz Band| Not Involved| total
---|---|---|---|---|---
Males| $0.20$| $0.02$| $0.08$| $0.10$| $0.4$
Females| $0.2$| $0.10$| $0.10$| $0.20$| $0.60$
Total| $0.4$| $0.12$| $0.18$| $0.30$| $1.00$

Now since we have created the bivariate table, we will find the relative frequency of students not involved in any activity.
From the table we can see that the frequency of students not involved in any activity is $0.30$ in which the frequency of male students is $0.10$ and female students is $0.20$, which is the required solution.

Note: A bivariate frequency is the type of frequency in which there are $2$variables rather than $1$ variable.
A distribution is considered to be bivariate when the distribution can be represented as a product of $2$ variables which have no correlation between them which means they are totally independent of each other.
In the above question the $2$ variables are Male students and female students, which are $2$ variables which are not dependent on each other.