Consider the following information regarding the performance of a class of 1000 students in four different tests: If a student scores 74 marks in each of the four tests, In which one of the following tests is her performance the best comparatively?
- ATest ICorrect
- BTest II
- CTest III
- DTest IV
Explanation
To compare performance across different tests where the class average and score spread (standard deviation) might vary, we use the Z-score (standard score). The Z-score is calculated as:
Z-score = (Student's Score - Class Mean) / Class Standard Deviation
A higher Z-score indicates better performance relative to the rest of the class in that particular test.
Since the student scored 74 marks in each test and Test I is identified as her best comparative performance, it implies that the Z-score for Test I must be the highest among all four tests. This means that in Test I, her score of 74 was relatively much higher above the class average, considering the standard deviation of scores, compared to her performance in the other tests. For example, if the class mean for Test I was significantly lower than 74 and the standard deviation was small, her Z-score for Test I would be highest.
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