Mason mistakenly calculated the conditional relative frequency for female students who prefer playing sports to be \(21 \%\). Here’s what Mason actually calculated and what he should have done differently:
First, let's break down the relevant statistics:
1. Total number of students: 87
2. Number of female students: 53
3. Number of female students who prefer playing sports: 18
### Mason's Calculation:
Mason calculated the percentage of the total number of students that are female and prefer playing sports. This is determined by dividing the number of female students who prefer playing sports by the total number of students and then multiplying by 100 to get the percentage.
[tex]\[ \text{Mason's calculation} = \left( \frac{18}{87} \right) \times 100 \approx 20.69\% \][/tex]
So, Mason calculated the joint relative frequency of female students who prefer playing sports among all students, not just among the female students.
### Correct Calculation:
The correct measure Mason was supposed to calculate is the conditional relative frequency, which should be the percentage of female students who prefer playing sports out of the total number of female students. This involves dividing the number of female students who prefer playing sports by the total number of female students and then multiplying by 100.
[tex]\[ \text{Correct calculation} = \left( \frac{18}{53} \right) \times 100 \approx 33.96\% \][/tex]
Thus, the conditional relative frequency for female students who prefer playing sports is approximately \(34\%\).
### Summary:
- Mason calculated the joint relative frequency of female students who prefer playing sports.
- The correct conditional relative frequency Mason should have calculated for female students who prefer playing sports is approximately \(34\%\).
Therefore, the correct statement from the given options is:
He calculated the joint relative frequency of female students who prefer playing sports. The conditional relative frequency for female students who prefer playing sports is [tex]\(34\%\)[/tex].
