Question

Bobby and Cindy are in different math classes. Bobby got a 75 on his test and Cindy got a 70 (surprisingly low for children of an architect). Bobby’s class had a mean of 80 and a standard deviation of 5. Cindy’s class had a mean of 75 and a standard deviation of 10. Who did better on their test, Bobby or Cindy?

Answer 1

Well since Bobby got a 75 on his test and Cindy got a 70, Bobby got a higher score. Unless I'm missing something, you are given the answer already.

Answer 2

Based on the same question, Suppose Bobby and Cindy’s neighbor was in Cindy’s class and was told that he scored at the 50th percentile in his class. What was his test score?

Answer 3

That first answer isn't correct.

Answer 4

or at least it may not be...

It may be asking, who did better compared to their own class mean?

Answer 5

Seems unlikely a question of mean and standard deviation would provide the answer in the question itself...

Answer 6

Bobby's score was one standard deviation below his class mean. Cindy's score was only half of a standard deviation below. Even though Cindy's score was lower, she was closer to her class mean.

The problem could be super simple as 75 > 70 Bobby > Cindy. But often problems like this are relevant when one class had a harder test. By comparing against the class mean, you don't penalize Cindy for getting a harder test than Bobby's class got.

Answer 7

(that should have read 75 > 70 or "Bobby > Cindy"

Answer 8

So, bobby did better in the test then