Question

(05.05 mc)
the table shows preferences of dancing or playing sports for male and female students:
do you prefer dancing or playing sports?
mason mistakenly calculated the conditional relative frequency for female students who prefer playing sports to be 21%. what statistic did mason actually calculate, and what should he have done differently?
○ he calculated the marginal relative frequency of female students who prefer playing sports. the conditional relative frequency for female students who prefer playing sports is 34%.
○ 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 50%.
○ he calculated the marginal relative frequency of female students who prefer playing sports. the conditional relative frequency for female students who prefer playing sports is 50%.
○ 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 34%.

Explanation:

Step1: Calculate Mason's 21% value

$\frac{18}{87} \approx 0.207$, or ~21%. This is the joint relative frequency (female who prefer sports divided by total students).

Step2: Calculate correct conditional frequency

Conditional relative frequency for female students who prefer sports uses the female student total as the denominator:
$\frac{18}{53} \approx 0.34$, or 34%.

Step3: Match to correct option

Mason calculated joint relative frequency; the correct conditional value is 34%.

Answer:

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 34%.