Question

Male and female students were surveyed about dancing and playing sports. They had the following preferences:

Do you prefer dancing or playing sports?
Playing sports Dancing Row totals
Male students 0.25 0.27 0.52
Female students 0.17 0.31 0.48
Column totals 0.42 0.58 1


Which of the following is a two-way conditional relative frequency table for gender?

Do you prefer dancing or playing sports?
Playing sports Dancing
Male students 0.60 0.47
Female students 0.40 0.53
Column totals 1 1

Do you prefer dancing or playing sports?
Playing sports Dancing Row totals
Male students 0.48 0.52 1
Female students 0.35 0.65 1

Do you prefer dancing or playing sports?
Playing sports Dancing Row totals
Male students 25% 27% 52%
Female students 17% 31% 48%
Column totals 42% 58% 100%

Do you prefer dancing or playing sports?
Playing sports Dancing Row totals
Male students 50 54 104
Female students 34 62 96
Column totals 84 116 200

Answer 1

The answer is B

Step-by-step explanation:

The second option

Answer 2

Answer: Choice B

`\begin{array}c \cline{1-4}& \text{Playing sports} & \text{Dancing} & \text{Row totals}\\ \cline{1-4}\text{Male students} & 0.48 & 0.52 & 1\\ \cline{1-4}\text{Female students} & 0.35 & 0.65 & 1\\ \cline{1-4}\end{array}`

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Step-by-step explanation:

For each row separately, divide the values by the row totals.

For instance, we divide the 0.25 (upper left corner) by the row total 0.52 to get 0.25/0.52 = 0.48 approximately. This is done for every item in every row. Even the row totals get the same thing happening to them which is why the "1"s are at the very end (eg: 0.52/0.52 = 1). They represent 100%

A result of 0.48 in the upper left corner means 48% of the men prefer playing sports and the 0.52 means 52% of the men prefer dancing.

Notice how 0.48+0.52 = 1.00 = 100% to account for all the men. The women's values in row 2 are calculated in a similar fashion.