Question

1. the two - way frequency table shows the number of students who participate in school sports or clubs at monroe high school.

sports or clubs no sports or clubs total
freshmen 48 60
sophomores 60 72
juniors 51 69
seniors 57 63
total 480
a. construct a relative frequency table by converting the data in the table to percentages. round to the nearest tenth if necessary.
b. find the joint relative frequency of a sophomore who participates in school sports or clubs.
c. what percentage of freshmen do not participate in school sports or clubs?
d. what percentage of seniors participate in school sports or clubs?

Explanation:

Step1: Calculate relative - frequencies for the table

To get the relative - frequency of each cell, divide the cell value by the total number of students (480).
For freshmen in sports or clubs: $\frac{48}{480}=0.1$
For freshmen not in sports or clubs: $\frac{60}{480}=0.125\approx0.1$
For sophomores in sports or clubs: $\frac{60}{480}=0.125\approx0.1$
For sophomores not in sports or clubs: $\frac{72}{480}=0.15$
For juniors in sports or clubs: $\frac{51}{480}=0.10625\approx0.1$
For juniors not in sports or clubs: $\frac{69}{480}=0.14375\approx0.1$
For seniors in sports or clubs: $\frac{57}{480}=0.11875\approx0.1$
For seniors not in sports or clubs: $\frac{63}{480}=0.13125\approx0.1$
The row - totals and column - totals are also calculated in the same way.

Step2: Find the joint relative frequency for part b

The joint relative frequency of a sophomore who participates in school sports or clubs is the value in the "Sophomores" row and "Sports or Clubs" column of the relative - frequency table. From step 1, it is $\frac{60}{480}=0.125\approx0.1$.

Step3: Find the percentage for part c

The percentage of freshmen who do not participate in school sports or clubs is the value in the "Freshmen" row and "No Sports or Clubs" column of the relative - frequency table. From step 1, it is $\frac{60}{480}=0.125 = 12.5\%\approx12.5\%$.

Step4: Find the percentage for part d

The percentage of seniors who participate in school sports or clubs is the value in the "Seniors" row and "Sports or Clubs" column of the relative - frequency table. From step 1, it is $\frac{57}{480}=0.11875 = 11.875\%\approx11.9\%$.

The relative - frequency table is:

	Sports or Clubs	No Sports or Clubs	Total
Sophomores	$0.1$	$0.15$	$0.275$
Juniors	$0.1$	$0.1$	$0.25$
Seniors	$0.1$	$0.1$	$0.225$
Total	$0.45$	$0.55$	$1$

Answer:

a. See the relative - frequency table above.
b. $0.1$
c. $12.5\%$
d. $11.9\%$