Question

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%.

Explanation:

Step1: Recall definitions

Joint relative frequency is the ratio of the frequency in a particular category to the total number of data - points. Conditional relative frequency is the ratio of the frequency in a particular category to the total number of data - points in a related sub - group. Marginal relative frequency is the sum of the joint relative frequencies in a row or a column.

Step2: Analyze the table

The value 20.7% in the table represents the proportion of 10th - grade students taking Geometry out of the total number of students. This is the joint relative frequency of 10th - grade students in Geometry.

Step3: Analyze the student's calculation

The student calculated $\frac{20.7\%}{29\%}\approx71.4\%$. This is the conditional relative frequency of 10th - grade students given that they are in Geometry (since 20.7% is the number of 10th - grade Geometry students and 29% is the total number of Geometry students).

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%.