Question

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

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 row - totals

Freshmen total: $48 + 60=108$
Sophomores total: $60 + 72 = 132$
Juniors total: $51+69 = 120$
Seniors total: $57 + 63=120$
Column - total for Sports or Clubs: $48+60 + 51+57=216$
Column - total for No Sports or Clubs: $60 + 72+69+63 = 264$

Step2: Construct relative - frequency table

For relative frequencies, divide each cell value by the grand - total (480).

	Sports or Clubs	No Sports or Clubs	Total
Sophomores	$\frac{60}{480}=0.125$	$\frac{72}{480}=0.15$	$\frac{132}{480}=0.275$
Juniors	$\frac{51}{480}\approx0.106$	$\frac{69}{480}\approx0.144$	$\frac{120}{480}=0.25$
Seniors	$\frac{57}{480}\approx0.119$	$\frac{63}{480}=0.131$	$\frac{120}{480}=0.25$
Total	$\frac{216}{480}=0.45$	$\frac{264}{480}=0.55$	1

Step3: Find joint relative frequency of a sophomore who participates in school sports or clubs

The joint relative frequency of a sophomore who participates in school sports or clubs is $\frac{60}{480}=0.125 = 12.5\%$

Step4: Find percentage of freshmen who do not participate in school sports or clubs

The percentage of freshmen who do not participate in school sports or clubs is $\frac{60}{108}\times100\%\approx55.6\%$

Step5: Find percentage of seniors who participate in school sports or clubs

The percentage of seniors who participate in school sports or clubs is $\frac{57}{120}\times100\% = 47.5\%$

Answer:

a. Relative - frequency table:

	Sports or Clubs	No Sports or Clubs	Total
Sophomores	12.5%	15.0%	27.5%
Juniors	10.6%	14.4%	25.0%
Seniors	11.9%	13.1%	25.0%
Total	45.0%	55.0%	100.0%

b. 12.5%
c. 55.6%
d. 47.5%