Question

Deanna collected data on the favorite sports of the students of two grades. The table shows the relative frequencies of rows for the data collected:

Favorite Sport
Swimming Running Volleyball Row totals
Grade 8 0.14 0.18 0.22 0.54
Grade 9 0.17 0.24 0.05 0.46
Column totals 0.31 0.42 0.27 1


Based on the data, which statement is most likely correct?
In Grade 8, 14 students liked swimming.
In Grade 9, 31% of students liked swimming.
In Grade 8, 22% of students liked volleyball.
In Grade 9, 5 students liked volleyball.

Answer 1

In Grade 8, 22% of students liked volleyball.

Explanation:

Given:

The table representing the relative frequencies of different sports in different grades among the students.

Swimming Running Volleyball Row totals

Grade 8 0.14 0.18 0.22 0.54

Grade 9 0.17 0.24 0.05 0.46

Column totals 0.31 0.42 0.27 1

Relative frequency gives the ratio of the number of quantities of a particular kind and the total number of quantities.

`\textrm{Relative frequency}=\frac{\textrm{Number of students in a particular sport}}{\textrm{Total students}}`

From the above table, we can conclude the following points:

Grade 8:

14% liked swimming, 18% liked running and 22% liked volleyball. So, a total of 54% students liked playing sports.

Grade 9:

17% liked swimming, 24% liked running and 5% liked volleyball. So, a total of 46% students liked playing sports.

Combining students of grade 8 and 9:

31% liked swimming, 42% liked running and 27% liked volleyball.

From all the options available, we observe that, third option is only correct.

In Grade 8, 22% of students liked volleyball.