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
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 for 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%.
is it a or c
It is option C. Mason mistakenly calculated the marginal relative frequency of female students who prefer playing sports instead of calculating the conditional relative frequency. The correct conditional relative frequency for female students who prefer playing sports is 50%.
The correct answer is c) 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%.
To determine this, we can refer to the table provided. The table shows the preferences of dancing or playing sports for male and female students.
Mason mistakenly calculated the relative frequency of female students who prefer playing sports as 21%. However, to find the conditional relative frequency of female students who prefer playing sports, we need to consider the females who prefer playing sports relative to the total number of females.
According to the table, the total number of female students is 53, and out of them, 18 prefer playing sports. Therefore, the correct calculation for the conditional relative frequency of female students who prefer playing sports is:
(18 / 53) * 100 = 33.96% ≈ 34%.
Therefore, Mason actually calculated the marginal relative frequency (18 out of the total 87) instead of the conditional relative frequency, which is why his answer is incorrect. The correct conditional relative frequency for female students who prefer playing sports is 34%, not 50% or any other given option.