Question

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%.

Answer 1

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%.

Answer 2

Female students Playing sports=18 Dancing=35 Total= 53

As, it is given that ,Conditional relative frequency for female students who prefer playing sports to be 21%.

It is Wrong value.

Joint Relative frequency for female students who prefer playing sports

`\frac{\text{ Playing sports}}{\text{Total Female}}\\\\=(18)/(87)* 100=21`

Conditional relative frequency
`=\frac {\text{Joint relative frequency}} {\text{Related marginal relative frequency.}}`

Related marginal relative frequency
`=\frac{\text{Total female who play sports or dance}}{\text{Total student}}\\\\=(53)/(87)`

Conditional relative frequency
`=(18)/(87)`=34% (approx)

Option D: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%.