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Assessing Z-Scores and Outliers

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1. Thousands of students apply for admission to graduate schools in economics each year with the intention of obtaining a PhD. The mean and standard deviation of these 129 productivity scores were used to compute a z score for each economics program. Harvard University had the highest z score (z=5.08) and hence was the top ranked school; Howard University was ranked last with the lowest z score (z+-0.81).
a. Interpret the z score for Harvard
b. Interpret the z score for Howard
c. The authors of the southern economic journal article note that only 44 out of 129 schools have positive z scores indicating that the distribution of overall productivity is skewed to the right. Do you agree? (check your answer by constructing a histogram for the z scores in the file attached.)

2. A sample data set has a mean of 57 and a standard deviation of 11. Determine whether each of the following sample measurements are outliers
a. 65
b. 21
c. 72
d. 98.

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The solution assesses the z-scores and outliers.

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1. a) It means that the economics program at Harvard is ...

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