120PM12A - Midterm 1 Practice Problems Answer Key...

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Midterm 1 Practice Problems Answer Key- Econometrics 120A 1. The following is a list of average SAT scores for graduating senior in different states State SAT Score Iowa 1810 Maine 1390 California 1510 Alabama 1680 Georgia 1470 South Dakota 1760 (a) What is the average SAT score across the listed states? This is just (1810 + 1390 + 1510 + 1680 + 1470 + 1760) / 6 = 1603 . 3. (b) What is the median SAT score in the above list? Ordering the data from smaller to larger we get: { 1390 , 1470 , 1510 , 1680 , 1760 , 1810 } . The me- dian is the smallest observation whose percentile is still larger than 0 . 5. Here the answer is 1510. Notice that this is the 50 th percentile, and in fact so is any number A such that 1510 A < 1680. For this reason we’ll accept any such number as an acceptable answer. (c) Is your answer to (b) the 50 th percentile of the sample? If yes, is your answer to (b) the only number that is a 50 th percentile? See the answer to part (b). (d) The mean square deviation of the above sample is 24,189. What is the variance? The difference between the mean square deviation and the variance is that in the former we divide by N , while in the latter we divide by N - 1. Hence we have Var = N N - 1 × 24 , 189 = 6 5
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