Which score has a higher relative position, a score of 43.5 on a test with a mean of 30 and a standard deviation of 9, or a score of 304 on a test with a mean of 226 and a standard deviation of 52? (Assume that the distributions being compared have approximately the same shape.)
A)A score of 304
B)A score of 43.5
C)Both scores have the same relative position.

Question

Which score has a higher relative position, a score of 43.5 on a test with a mean of 30 and a standard deviation of 9, or a score of 304 on a test with a mean of 226 and a standard deviation of 52? (Assume that the distributions being compared have approximately the same shape.) 
A)A score of 304
B)A score of 43.5
C)Both scores have the same relative position.

Quizplus · Accepted Answer

To determine the relative position of each score, we calculate the z-score for each. The z-score is calculated as (score - mean) / standard deviation. For the first score: (43.5 - 30) / 9 = 1.5. For the second score: (304 - 226) / 52 = 1.5. Both scores have a z-score of 1.5, indicating they have the same relative position within their respective distributions.

Which Score Has a Higher Relative Position, a Score of 43.5