Question

question 2 of 25
the ages and grades of some of the 19 girls on a club soccer team are shown in the table.

	15 years old	16 years old
10th grade		10

which two - way frequency table correctly shows the marginal frequencies?
a.

	15 years old	16 years old	total
10th grade	7	10	17
total	9	10	19

b.

	15 years old	16 years old	total
10th grade	9	10	19
total	11	10	21

c.

	15 years old	16 years old	total
10th grade	17	10	27
total	19	10	29

d.

	15 years old	16 years old	total
10th grade	7	10	17
total	10	10	19

Explanation:

Step1: Analyze total number of girls

The total number of girls is 19, so the grand total in the two - way table should be 19. Let's check the grand totals of each option:

• Option A: Grand total is \(9 + 10=19\)
• Option B: Grand total is \(11+10 = 21

eq19\)

• Option C: Grand total is \(19 + 10=29

eq19\)

• Option D: Grand total is \(10+10 = 20

eq19\)

Step2: Analyze the number of 10th grade girls

We know that in 16 - year - old, 10th grade has 10 girls. Let the number of 15 - year - old 10th grade girls be \(x\). The total number of 10th grade girls is \(x + 10\), and the total number of 9th grade girls is 2. So \(2+(x + 10)=19\), which gives \(x+12 = 19\), so \(x = 7\). Also, the total number of 15 - year - old girls is \(2 + 7=9\) and the total number of 16 - year - old girls is \(0 + 10 = 10\).

Now let's check each option:

• Option A: 15 - year - old total is \(2 + 7=9\), 16 - year - old total is \(0+10 = 10\), 9th grade total is 2, 10th grade total is \(7 + 10=17\), grand total is \(9+10 = 19\). This matches.
• Option B: Grand total is 21 (incorrect), 15 - year - old total is \(2 + 9=11\) (incorrect as we calculated 9)
• Option C: Grand total is 29 (incorrect)
• Option D: 15 - year - old total is \(2+7 = 9

eq10\) (incorrect)

Answer:

A.

	15 years old	16 years old	Total
10th grade	7	10	17
Total	9	10	19