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03 STAT HWA a - Dr Valerie R Bencivenga Economics 329...

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Dr. Valerie R. Bencivenga Economics 329 PRACTICE HOMEWORK #3A: ANSWERS 1.a. b. b. Symmetric unimodal distribution Symmetric distribution Negatively skewed mean = median = mode with no mode mean < median < mode c. d. e. X X Y X Y Y 2.a. 413 ) 400 500 )( 78 . 13 4815 . 5 . ( 400 median b. 632 ) 600 700 )( 1028 . 4673 . 5 . ( 600 student median by attended size c. This is the IQ range of the second distribution (percentage of students, not percentage of schools). 426 ) 400 500 )( 1261 . 2172 . 25 . ( 400 quartile st 1 987 ) 800 1000 )( 1053 . 6517 . 75 . ( 800 quartile rd 3 IQ range = 987 426 = 561 d. K 1 k k k X f X where X k = midpoint of the k th class, and f k = proportion of observations in the k th class: ) 0013 (. 4000 ) 0099 (. 2500 ... ) 129 (. 250 ) 1131 (. 150 ) 901 (. 50 X ) 0013 (. ) X 4000 ( ) 0099 (. ) X 2500 ( ... ) 129 (. ) X 250 ( ) 1131 (. ) X 150 ( ) 901 (. ) X 50 ( s 2 2 2 2 2 2 X There are 13 class intervals, so there are 13 terms in each sum.
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3.a. When calculating the median (or any other percentile), we assume that the observations in a class are evenly (uniformly) distributed along the class interval. Probably the observations in the lowest class interval are not evenly distributed from 0 to <100. Probably there are relatively more schools in the upper end of this interval than in the lower end (i.e., more schools with 80 to <100 than
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