120PM15A - Midterm 1 Practice Problems Answer Key...

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1. The following is a list of starting median salaries for college graduates by profession: Degree Starting Median Salary Chemical Engineering 65,700 Finance 48,500 Economics 50,200 Statistics 48,600 Computer Science 56,400 (a) What is the average starting salary across the college degrees listed? This is just (65 , 700 + 48 , 500 + 50 , 200 + 48 , 600 + 56 , 400) / 5 = 53 , 880. (b) What is the 80 th percentile of the above sample? Ordering the observations from smallest to largest: { 48 , 500 , 48 , 600 , 50 , 200 , 56 , 400 , 65 , 700 } . The 80 th percentile is a number “ A ” such that (# obs A ”) / 5 = 0 . 8. This implies that (# obs A ”) = 4, or equivalently that “ A ” must the be 4 th largest observation: 56,400. (c) Is your answer to (b) unique? Justify your answer. It is important to notice that in fact any number “ A ” satisfying 56 , 400 A < 65 , 700 would yield (# obs A ”) / 5 = 0 . 8. For this reason, sometimes percentiles are defined as the smallest number which satisfies this property, in this case: 56 , 400. (d) For the above sample, what is larger: the Variance or the Mean Squared Deviation? You don’t need to do any calculations here. The variance is always larger than the mean squared deviation, as the former divides by N - 1, while the latter divides by N . (e) The Mean Absolute Deviation for the above sample is 5 , 736. What would the mean absolute deviation be if everybody made 5,000 less dollars? Justify your answer.
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