Question

The following two-way table shows the data for the students of two different grades in a school:

Based on the relative row frequency, the students of which grade are more likely to be members of the school band?

Grade 7
Grade 8
The students of both grades are equally likely to be members of the school band
No conclusion can be drawn about the chances of a student being a member of the school band

Answer 1

Based on the relative row frequency, the students of Grade 8 are more likely to be members of the school band.

Explanation:

The relative row frequency is obtained by dividing each entry of by the corresponding row total.

i.e. the first row is obtained by dividing each entry of the first row by the row total.

Similar process holds for second row and third row.

Here on obtaining the relative row frequency we have:

The relative row frequency that a Grade 7 student like to be a member of school band= 0.56

and the relative row frequency that a Grade 8 student like to be a member of school band= 0.83

Since, 0.83>0.56

Hence, we have:

Grade 8 student is likely to be a member of school band.

Answer 2

There are 18 students in Grade 7, 10 are in band, so 10/18 = 0.56 are in band.

There are 12 students in Grade 8, 10 are in band, so 10/12 = 0.83 are in band.

Students in Grade 8 are more likely to be members of the band.