Question

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
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 part a

For each cell, divide the cell value by the total number of students (480).
For example, for freshmen in sports or clubs: $\frac{48}{480}=0.1$.

Step2: Find joint relative frequency for part b

The number of sophomores in sports or clubs is 60. The joint relative frequency is $\frac{60}{480}=0.125$.

Step3: Calculate percentage for freshmen not in sports or clubs for part c

The number of freshmen not in sports or clubs is 60. The percentage is $\frac{60}{480}\times100 = 12.5\%$.

Step4: Calculate percentage for juniors in sports or clubs for part d

The number of juniors in sports or clubs is 51. The percentage is $\frac{51}{480}\times100=\frac{5100}{480}\approx10.6\%$.

Answer:

a.

	Sports or Clubs	No Sports or Clubs	Total
Sophomores	0.125	0.15	0.275
Juniors	0.106	0.144	0.25
Seniors	0.119	0.131	0.25
Total	0.45	0.55	1

b. 0.125
c. 12.5%
d. 10.6%