Question

The two-way table shows the results of a survey about high school students' music preferences. Which graph correctly displays the relative frequencies of the three types of music shown in the two-way table?

Answer 1

Answer: Fourth graph.

Country: C=251 (left bar)
Rap: R=398 (middle bar)
Rock: K=366 (right bar)

The middle bar must be the higher, then the second graph is not an option.

Taking the middle bar as reference:

In the first graph:
A number of units in the graph of the middle bar: 14
The left bar should have:
(251/398)(14)=(0.63)(14)=8.82=9 units, and it has in the graph only 6 units, then it's not the first graph.

In the third graph:
A number of units in the graph of the middle bar: 9.5
The left bar should have:
(251/398)(9.5)=(0.63)(9.5)=5.99=6 units, and it has in the graph only 4 units, then it's not the third graph.

In the fourth graph:
A number of units in the graph of the middle bar: 7.5
The left bar should have:
(251/398)(7.5)=(0.63)(7.5)=4.7=5 units, and it has in the graph 5 units.
The right bar should have: (366/398)(7.5)=(0.92)(7.5)=6.9=7 units, and it has in the graph 7 units

Answer: Fourth graph

Answer 2

Answer with explanation:

We are given a two-way table that represents the frequency of three types of music.

Hence, the relative frequency table is given by:

Female Male Total

Country 145/1015 106/1015 251/1015

Rap 158/1015 240/1015 398/1015

Rock 214/1015 152/1015 366/1015

Total 517/1015 498/1015 1015/1015

Female Male Total

Country 0.143 0.104 0.247

Rap 0.155 0.237 0.392

Rock 0.211 0.150 0.361

Total 0.509 0.491 1

Hence, clearly we could see that the relative frequency of the music country is much low as compared to that of Rock and rap.

Hence, there is a much difference between the bar of Country as compared to Rock and rap.

and there is a low difference between the bar of rock and rap.