question is in description

Question

Analia is a school district manager. Here are some details about two schools in her district for the last school year: School A School B Number of students 300030003000 400040004000 Number of teachers 190190190 380380380 Graduation rate 86\%86%86, percent 90\%90%90, percent Budget per student \$10{,}500$10,500dollar sign, 10, comma, 500 \$10{,}000$10,000dollar sign, 10, comma, 000 % of students in sports club 62\%62%62, percent 68\%68%68, percent Number of sports medals won 999 777 SAT average 120012001200 105010501050 SAT range (max-min) 900900900 700700700 Analia wants to know which school has the higher SAT average relative to the resources invested per student. 1) Analia thought of two different ways to define this quantity. Identify these two definitions among the following options. Choose 2 answers: Choose 2 answers: (Choice A) A SAT average divided by number of sports medals won (Choice B) B SAT average divided by number of students (Choice C) C SAT average divided by budget per student (Choice D) D SAT average divided by teachers per student 2) 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: Choose 1 answer: (Choice A) A Yes. According to both definitions, school A has the higher SAT average relative to the resources invested per student. (Choice B) B Yes. According to both definitions, school B has the higher SAT average relative to the resources invested per student. (Choice C, Checked) C No. The definitions have opposite results.

Answer 1

Hello Amber S.,

My name is Andrew, I hope I am understanding this question correctly because I see the question appears to have some repeating numbers. This may be how I am viewing this question. If I understood the number correctly then I think I may have a solution and my reasoning behind my solution is as follows:

I have interpreted the answer to be these three options:

Answer 1. school A has a higher SAT to relative resources per student

Answer 2. school B has a higher SAT to relative resources per student

Answer 3. no the definitions have opposite results.

Choosing one of the as the answers is based on the calculations between school A or school B. These are my results assuming I interpreted the numbers correctly:

Option A : school A = 1.20 school B = 1.35

Option B: school A = 0.40 school B = 0.26

Option C : school A = 0.11 school B = 0.11

Option D: school A = 18,947.4 school B = 11,052.6

I am making a big assumption in my analysis that the larger the numbers means more resources per student.

So if I understand the question and am interpreting the numbers correctly, two of the options A, B, C, or D need to make sense when determining Answer 1, 2, or 3.

I would approach this question by looking at options A, B, C, and D and determining if school A number is greater than school B number.

1.20 < 1.35 school B wins

0.40 > 0.26 school A wins

0.11 = 0.11 tie, within 2 decimal places

18,947 > 11,052 school A wins

If we pick answer 2 where school B has more resources, then we would have to show what two options where school B is greater than school A. Looking at the numbers I calculated above I do not see two choices where school B is greater than school A, only 1 option and a tie.

If we pick answer 3 where none of the answers are greater or they do not make sense then this answer can be chosen.

If we pick answer 1 where school A has more resources then we would have to pick options B and D. Again this is assuming I am interpreting the numbers provided are just repeating. this means that school A is the correct choice.

Note: I would also like to point out that part D is slightly difficult for me to determine without a comma because this choice could be interpreted two very different ways. The way I interpret this is: SAT average / (teachers / student). However, with no comma someone might interpret this choice to be (SAT average / teachers) / student. My assumption is that the usage of "per" connects the two words teachers and student together. The other interpretation is: school A: 0.0021 and school B: 0.00069 and for this scenario the results are still the same where 0.0021 > 0.00069.

I hope that I have helped answer this question and please if you have another question as to how I got a number or don't understand please leave a comment or contact me through this system and I will do my best to explain an answer.

How I derived the numbers that lead to my decision is the following:

Option A, school A : SAT avg / medal = 1200/999 = 1.20

Option A, school B : SAT avg / medal = 1050/777 = 1.35

Option B, school A : SAT avg / medal = 1200/3000 = 0.40

Option B, school B : SAT avg / medal = 1050/4000 = 0.26

Option C, school A : SAT avg / medal = 1200/10,500 = 0.11

Option C, school B : SAT avg / medal = 1050/10,000 = 0.11

Option D, school A : SAT avg / medal = 1200/(190/3000) = 18,947.37

Option D, school B : SAT avg / medal = 1050/(380/4000) = 11,052.63