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?

playing sports

dancing

row totals

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male students

18

16

34

female students

18

35

53

column totals

36

51

87

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:

1. First, calculate the value Mason got: $21\% = \frac{18}{87} \times 100\%$. This is the joint relative frequency (female who prefer sports divided by total students).
2. Calculate the correct conditional relative frequency: it is the number of female students who prefer sports divided by the total number of female students: $\frac{18}{53} \times 100\% \approx 34\%$.
3. Match this to the correct option.

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%.