Explain the general rationale behind using a z -score for describing how an indi

Question

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.

Explanation / Answer

Question 1

A z-score describes how the individual has fared in the test as compared to the others. With a z-score, we know what % of students have scored lower or higher than this student.

With only the mean and individual score, it is not possible to ascertain if he is relatively good or not.

Question 2)

The z-score gives an idea of what percentage of population is above or below the individual. A z-score of 0.67449 indicates the 25th percentile of the normal distribution. All z-scores above 0.67449 are of subjects in the target range.

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