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 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.

     

Answer 2

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