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# ECO 430 Sample Variance of Average Study Problems

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ECO 430 Problem Set 1 Solutions Question 1 (a) We have 3 observations, so the sample size is 3. (b) Let’s denote hourly earnings by Y . Then, the sample average hourly earnings, denoted by Y , are: Y = (30 + 20 + 22)=3 = 24 (c) If we rearrange the observed hourly earnings in ascending order, we have 20, 22, 30. The sample median is the value in the middle, i.e., 22. [Note that if the sample size is an even number, then there will be the two values in the middle (after rearranging the observations in ascending order) and the sample median will be the average of these two values.] (d) The sample variance of average hourly earnings equals: 3 X 2 2 2 2 Yi Y = (30 24) +(20 224) +(22 24) = 28 s2Y = 3 1 1 i=1 The unit of measurement is dollars dollars, i.e., squared dollars. p (e) The p sample standard deviation of average hourly earnings equals sY = s2Y = 28 5:29. The unit of measurement is dollars. (f) Let’s denote years of education by X. Note that X = (20 + 16 + 12)=3 = 16. Then, the sample covariance between average hourly earnings and years of education equals: 3 X sXY = 3 1 1 Xi X Yi Y i=1 16)+(22 24)(12 16) = (30 24)(20 16)+(20 24)(16 = 16 2 The unit of measurement is dollar ...
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