SOLUTION: Explain the general rationale behind using a z-score for describing how an individual performed on an exam compared to just stating the overall mean and the individual's score. How

Question 1116934: Explain the general rationale behind using a z-score for describing how an individual performed on an exam compared to just stating the overall mean and the individual's score. How does the information differ in the two situations? What additional information are you gaining with a z-score?
Imagine you are in charge of reviewing applications for your academic institution. As a preliminary measure, you want to review only the top 25% of applicants on the basis of standardized test scores. How does calculating the z-score provide additional information regarding how each subject did overall? Provide specific examples of how you would use the information and interpret the scores.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The z-score gives a standardized value of where the individual's score was among all the others.
If the mean were 68 and the individual got a 75, that is above the mean. But if the z-score were .25, that would suggest the individual is slightly above the mean. If the z-score were 2, that would suggest the individual was in the top 5% of the class.
The top 25% of individuals is a z-score of about +0.67. With this information, one can look at the score in light of the variability in the exam, and z-scores of -1,-2,1,2 are very easy to understand in forming percentiles.
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