Question

12th grade Math: Two-Way Frequency Tables MC

Students at a virtual school are allowed to sign up for one math class each year. The numbers of students signing up for various math classes for the next school year are given in the following table:


Grade Geometry Algebra II Pre-Calculus AP Statistics Total
10th 20.7% 10.3% 3.4% 0.7% 35.2%
11th 6.7% 13.8% 10.3% 2.8% 33.8%
12th 1.4% 6.7% 13.8% 9% 31%
Total 29% 31% 27.6% 12.4% 1


A student calculated the joint relative frequency of 10th grade students in geometry as being 71.4%. What did the student actually calculate, and what is the correct answer?
The student calculated the conditional relative frequency for students who are in 10th grade, given that they are enrolled in Geometry. The correct value of the joint relative frequency of 10th grade students in geometry is 20.7%.
The student calculated the conditional relative frequency for students who are in 10th grade, given that they are enrolled in Geometry. The correct value of the joint relative frequency of 10th grade students in geometry is 29%.
The student calculated the marginal relative frequency for 10th grade students in geometry. The correct value of the joint relative frequency of 10th grade students in geometry is 20.7%.
The student calculated the marginal relative frequency for 10th grade students in geometry. The correct value of the joint relative frequency of 10th grade students in geometry is 29%.

Answer 1

the student most likely calculated (% of 10th grade students in geometry) / (% of all geometry students) = 20.7% / 29% = 71.4% which is *conditional* relative frequency that a student is in 10th grade given that they are in geometry. (notice how they divided the tenth grade geometry student population by the entire geometry population).

instead, they should simply divide (the % of tenth grade students in geometry) by the whole population 100%.