Question

identifying joint frequencies
a survey was conducted with high school students in each grade to see how many prefer math or science. some of the data are shown below.

	9	10	11	12	total
science	40		15	32	95
total	63	26	29	67	185

which statement is true about the joint frequencies in this table?

• twenty - three 9th graders and fifteen 11th graders prefer math.
• fourteen 11th graders prefer math and eight 10th graders prefer science.
• thirty - five 12th graders prefer math and nine 10th graders prefer science.
• twenty - three 9th graders and thirty - two 12th graders prefer math.

Explanation:

Step1: Calculate 9th graders who prefer math

Total 9th graders: 63. 9th graders who prefer science: 40. So math - 9th: \( 63 - 40 = 23 \).

Step2: Calculate 10th graders who prefer science

Total 10th graders: 26. 10th graders who prefer math: 18. So science - 10th: \( 26 - 18 = 8 \).

Step3: Calculate 11th graders who prefer math

Total 11th graders: 29. 11th graders who prefer science: 15. So math - 11th: \( 29 - 15 = 14 \).

Step4: Calculate 12th graders who prefer math

Total 12th graders: 67. 12th graders who prefer science: 32. So math - 12th: \( 67 - 32 = 35 \).

Step5: Evaluate each option

• Option 1: 11th math is 14 (not 15). Incorrect.
• Option 2: 11th math =14, 10th science=8. Correct.
• Option 3: 12th math is 35, but 10th science is 8 (not 9). Incorrect.
• Option 4: 12th math is 35 (not 32). Incorrect.

Answer:

Fourteen 11th graders prefer math and eight 10th graders prefer science.