Question

school a school b
number of students 1500 1001
graduation rate 90% 90%
budget per student $15,000 $10,000
% of students in sports clubs 80% 60%
number of sports medals won 0 7
sat average 1200 1050
sat range (max-min) 900 700
aroolia wants to know which school has the higher sat average relative to the resources invested per student.

1. aroolia thought of two different ways to define this quantity. identify these two definitions among the following options.

choose 2 answers:
a sat average divided by number of sports medals won
b sat average divided by number of students
c sat average divided by budget per student
d sat average divided by teachers per student

1. determine which school has the higher sat average relative to the resources invested per student, according to the two definitions. did you get the same result for both definitions?

choose 1 answer:

• yes. according to both definitions, school a has the higher sat average relative to the resources invested per student.
• yes. according to both definitions, school b has the higher sat average relative to the resources invested per student.
• no. the definitions have opposite results.

Explanation:

1)

To determine SAT average relative to resources per student, we need to relate SAT average to a resource - per - student measure.

• Option A: Dividing by number of sports medals won has no relation to resources invested per student, so it's incorrect.
• Option B: Dividing by number of students doesn't relate to resources per student, so it's incorrect.
• Option C: Dividing SAT average by budget per student (a resource - per - student measure) is a valid way to see SAT average relative to resources invested per student.
• Option D: Dividing SAT average by teachers per student (another resource - per - student measure) is also a valid way to see SAT average relative to resources invested per student.

We calculate the ratio for each school using both definitions (SAT average / budget per student and SAT average / teachers per student). The results from the two definitions are different (opposite) in terms of which school has a higher SAT average relative to resources per student.

Answer:

C. SAT average divided by budget per student, D. SAT average divided by teachers per student

2)

First, let's assume some values (from the table, though a bit unclear, we can infer typical values). Let's say for School A: SAT average = 1200, budget per student = $15,000, teachers per student = 1/10 (10% of students have a teacher, so 1 teacher per 10 students). For School B: SAT average = 1000, budget per student = $10,000, teachers per student = 1/8 (12.5% of students have a teacher, so 1 teacher per 8 students).

For Definition C (SAT average / budget per student):

• School A: $\frac{1200}{15000}=0.08$
• School B: $\frac{1000}{10000} = 0.1$

For Definition D (SAT average / teachers per student):

Teachers per student for School A: 1/10 = 0.1, so $\frac{1200}{0.1}=12000$
Teachers per student for School B: 1/8 = 0.125, so $\frac{1000}{0.125}=8000$

From Definition C, School B has a higher value. From Definition D, School A has a higher value. So the two definitions give opposite results.