DA0-001 · Question #69
Randy scored 76 on a math test, Katie scored 86 on a science test, Ralph scored 80 on a history test, and Jean scored 80 on an English test. The table below contains the mean and standard deviation…
The correct answer is B. Katie. To compare scores across different tests with varying means and standard deviations, Z-scores must be calculated to determine which student performed best relative to their respective class.
Question
Randy scored 76 on a math test, Katie scored 86 on a science test, Ralph scored 80 on a history test, and Jean scored 80 on an English test. The table below contains the mean and standard deviation of the scores for each of the courses:
Using this information, which of the following students had the BEST score?
Exhibit
Options
- ARandy
- BKatie
- CRalph
- DJean
How the community answered
(47 responses)- A11% (5)
- B79% (37)
- C6% (3)
- D4% (2)
Why each option
To compare scores across different tests with varying means and standard deviations, Z-scores must be calculated to determine which student performed best relative to their respective class.
Randy's Z-score for his math test is (76-70)/5 = 1.2, which is lower than Katie's Z-score, meaning his performance relative to his class was not as exceptional.
Katie's score of 86 on the science test, with a mean of 80 and standard deviation of 3, results in a Z-score of (86-80)/3 = 2.0. This Z-score is the highest among all students, indicating she performed the best relative to the average and spread of scores in her specific test.
Ralph's Z-score for his history test is (80-75)/4 = 1.25, which is lower than Katie's Z-score, indicating he did not perform as well relative to his class.
Jean's Z-score for her English test is (80-78)/2 = 1.0, which is lower than Katie's Z-score, meaning her performance relative to her class was not as strong.
Concept tested: Z-score calculation for comparative analysis
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