Question

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. 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: Analyze first option

Check number of 9th - graders and 11th - graders who prefer math. From the table, we need to find the intersection of 9th - grade column and Math row and 11th - grade column and Math row.
For 9th - graders who prefer math: \(63 - 40=23\). For 11th - graders who prefer math: \(29 - 15 = 14
eq15\). So this option is false.

Step2: Analyze second option

For 11th - graders who prefer math: \(29 - 15=14\). For 10th - graders who prefer science: \(26 - 18 = 8\). This option is true.

Step3: Analyze third option

For 12th - graders who prefer math: \(67 - 32=35\). For 10th - graders who prefer science: \(26 - 18 = 8
eq9\). So this option is false.

Step4: Analyze fourth option

For 9th - graders who prefer math: \(63 - 40 = 23\). For 12th - graders who prefer math: \(67 - 32=35
eq32\). So this option is false.

Answer:

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