Given the table:
| | Sunrise | No Sunrise | Total |
| :------ | :------ | :--------- | :---- |
| Sunset | 14 | 12 | 26 |
| No Sunset | 7 | 5 | 12 |
| Total | 21 | 17 | 38 |
Which is the joint relative frequency for the people who can only see the sunset?
A. [tex]$\frac{5}{38}$[/tex]
B. [tex]$\frac{7}{38}$[/tex]
C. [tex]$\frac{12}{38}$[/tex]
D. [tex]$\frac{14}{38}$[/tex]
Answer (1)
Identify the number of people who see the sunset but not the sunrise: 12.
Divide this number by the total number of people: 38 12 .
The joint relative frequency for people who can only see the sunset is 38 12 .
Explanation
Understand the problem We are given a table that shows the relationship between sunrise and sunset. We want to find the joint relative frequency for people who can only see the sunset. This means we are looking for people who see the sunset but do not see the sunrise.
Identify the relevant data From the table, we can see that there are 12 people who see the sunset but not the sunrise. The total number of people is 38.
Calculate the joint relative frequency The joint relative frequency is the number of people who see the sunset but not the sunrise divided by the total number of people. So, the joint relative frequency is 38 12 .
State the final answer Therefore, the joint relative frequency for people who can only see the sunset is 38 12 .
Examples
Understanding joint relative frequencies can help in analyzing survey data. For example, if you survey people about their coffee and tea preferences, you can create a table showing how many people like both, only coffee, only tea, or neither. The joint relative frequencies would then tell you the proportion of the total population that falls into each category, helping you understand the overall preferences of the group.
