Question

Students from two age groups were surveyed to see how they travel to school. Here are the results:

Below age 15—Walk or bike: 87; Bus: 60; Car: 18
Age 15 and above—Walk or bike: 65; Bus: 50; Car: 80

Which of the following is a correct two-way relative frequency table for the data?

Answer 1

The table representing the number of students by which mode of transport they travel is given as:

Walk or bike Bus Car Row Total

Below age 15 87 60 18 165

Age 15 and above 65 50 80 195

Column Total 152 110 98 360

We know that a relative frequency of an event is the ratio of frequency to the total number of trials.

i..e we divide each frequencies by 360 to obtain a two-way relative frequency.

Hence,the table is given as:

Walk or bike Bus Car Row Total

Below age 15 0.24 0.17 0.05 0.46

Age 15 and above 0.18 0.14 0.22 0.54

Column Total 0.42 0.31 0.27 1

Answer 2

Options:

A. Method of Travel to School

Walk/Bike Bus Car Row totals

Below age 15 87 60 18 165

Age 15 and above 65 50 80 195

Column totals 152 110 98 360

B. Method of Travel to School

Walk/Bike Bus Car Row totals

Below age 15 0.24 0.17 0.05 0.46

Age 15 and above 0.18 0.14 0.22 0.54

Column totals 0.42 0.31 0.27 1

C. Method of Travel to School

Walk/Bike Bus Car Row totals

Below age 15 0.52 0.36 0.11 1

Age 15 and above 0.33 0.26 0.41 1

Column totals 0.42 0.31 0.27 1

D. Method of Travel to School

Walk/Bike Bus Car Row totals

Below age 15 0.57 0.55 0.18 0.46

Age 15 and above 0.43 0.45 0.82 0.54

Column totals 1 1 1 1

The answer is option B as you can see this two way frequency table has the same data as in the question.

Hope this helps!