120PM11A - Midterm 1 Practice Problem Econometrics 120A 1...

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Midterm 1 Practice Problem - Econometrics 120A 1. The Big Mac Index is annually compiled by “The Economist” to compare exchange rates across different countries. The following is a sample of such list, containing the price of a Big Mac in US Dollars for a number of different countries. Country Price in US$ Indonesia 2.05 Norway 7.90 Iceland 6.00 Malaysia 1.70 Latvia 3.50 (a) What is the average price in dollars of a Big Mac? This is just (2 . 05 + 7 . 90 + 6 . 00 + 1 . 70 + 3 . 50) / 5 = 4 . 23. (b) What is the median price in dollars of a Big Mac? Ordering the data from smaller to larger we get: { 1 . 70 , 2 . 05 , 3 . 50 , 6 . 00 , 7 . 90 } . The median is the smallest observation whose percentile is still larger than 0 . 5. Here the answer is 3 . 50. (c) Is your answer to (b) the 50 th percentile of the sample? Is there a number that is the 50 th percentile of this sample? Note that the percentile of 3 . 50 is given by Number obs 3 . 50 N = 3 5 Hence 3.50 is not the 50 th percentile. Furthermore, there is no number that is the 50 th percentile. Any number greater than 3 . 50 must have a higher percentile than 3 / 5. On the other hand, any number between 2 . 05 and 3 . 50 will have percentile 2 / 5 < 0 . 5. (d) The current US$-Euro exchange rate is 0.75 (that is 1 Dollar buys you 0.75 Euros). What is the average price of a Big Mac in Euros?
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