Question

pretest: bivariate data
favorite course math english history science total
9th grade 78 26 130 117 351
10th grade 104 39 91 91 325
11th grade 65 52 117 78 312
12th grade 52 65 65 78 260
total 299 182 403 364 1,248
which of the following can be concluded from the joint and marginal frequencies of the table?
i. math is the most popular subject in the 10th grade
ii. history is the least popular subject in the 9th grade
iii. science is more popular than math among 12th grade students
iv. students in the 11th grade like english more than students in the 12th grade
v. the overall favorite course is history
a. ii and v only
b. i iii and v
c. ii and iv only
d. iii and iv only

Explanation:

Step1: Analyze 10th - grade preferences

In 10th grade, math has 104 students, English has 39 students, history has 91 students and science has 91 students. Since 104>91>39, math is the most popular subject in 10th grade.

Step2: Analyze 9th - grade preferences

In 9th grade, English has 26 students, which is the least among math (78), history (130) and science (117). So history is not the least popular subject in 9th grade.

Step3: Analyze 12th - grade preferences

In 12th grade, math has 52 students and science has 78 students. So science is more popular than math among 12th - grade students.

Step4: Analyze English preferences between 11th and 12th grades

In 11th grade, 52 students like English and in 12th grade, 65 students like English. So students in 12th grade like English more than students in 11th grade.

Step5: Analyze overall favorite course

The total number of students who like math is 299, English is 182, history is 403 and science is 364. Since 403>364>299>182, the overall favorite course is history.

Answer:

B. I, III and V