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 50
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?

what percentage of seniors participate in school sports or clubs?

Explanation:

Step1: Calculate row - totals

Freshmen total: $48 + 50=98$
Sophomores total: $60 + 72 = 132$
Juniors total: $51+69 = 120$
Seniors total: $57 + 63=120$
Grand - total: $480$

Step2: Calculate relative frequencies for each cell

Freshmen

Sports or Clubs: $\frac{48}{480}\times100\%\approx10.0\%$
No Sports or Clubs: $\frac{50}{480}\times100\%\approx10.4\%$

Sophomores

Sports or Clubs: $\frac{60}{480}\times100\% = 12.5\%$
No Sports or Clubs: $\frac{72}{480}\times100\%=15.0\%$

Juniors

Sports or Clubs: $\frac{51}{480}\times100\%\approx10.6\%$
No Sports or Clubs: $\frac{69}{480}\times100\%\approx14.4\%$

Seniors

Sports or Clubs: $\frac{57}{480}\times100\%\approx11.9\%$
No Sports or Clubs: $\frac{63}{480}\times100\%\approx13.1\%$

Totals

Sports or Clubs total: $\frac{48 + 60+51+57}{480}\times100\%=\frac{216}{480}\times100\% = 45.0\%$
No Sports or Clubs total: $\frac{50 + 72+69+63}{480}\times100\%=\frac{254}{480}\times100\%\approx52.9\%$

The 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	$45.0\%$	$52.9\%$	$100.0\%$

Step3: Answer part b

The joint relative frequency of a sophomore who participates in school sports or clubs is $\frac{60}{480}\times100\% = 12.5\%$

Step4: Answer part c

The percentage of freshmen who do not participate in school sports or clubs is $\frac{50}{98}\times100\%\approx51.0\%$

Step5: Answer part d

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

Answer:

a. See the relative - frequency table above.
b. $12.5\%$
c. $51.0\%$
d. $47.5\%$