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

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
Freshmen	$\frac{48}{480}=0.1$	$\frac{60}{480}=0.125$	$\frac{108}{480}=0.225$
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
Freshmen	10.0%	12.5%	22.5%
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%