solutions HMWK 1

solutions HMWK 1 - ISDS-361A & SD Panayiotis Skordi...

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ISDS-361A Homework 1. Mean, Median, Mode, Range, Variance Panayiotis Skordi 1. A basketball player has the following points for seven games: 20, 25, 32, 18, 19, 22, 30 Compute the following measures of central location: a. mean b. median c. mode Answers a. Mean 71 . 23 7 166 7 30 22 19 18 32 25 20 = = + + + + + + b. Median { } 32 30 25 22 20 19 18 c. Mode There is no mode. 1
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2. Consider the following population of measurements: 162, 152, 177, 157, 184, 176, 165, 181, 170, 163 a. compute the mean b. compute the median Answers a. Mean 70 . 168 10 1687 10 163 170 181 165 176 184 157 177 152 162 = = + + + + + + + + + b. Median 184 181 177 176 170 165 163 162 157 152 5 . 167 2 170 165 = + 3.The following data represent the number of children in a sample of 10 families from a certain community: 2
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4, 2, 1, 1, 5, 3, 0, 1, 0, 2 a. compute the range b. compute the variance c. compute the standard deviation Answers a. Range 5 0 5 = - b. Variance 1 ) ( 1 2 2 - - = = n x x s n i i Remember that 9 . 1 10 19 1 = = = = n x x n i i i i x x x i - 2 ) ( x x i - 1 4 2.1 4.41 2 2 0.1 0.01 3 1 -0.9 0.81 4 1 -0.9 0.81 5 5 3.1 9.61 6 3 1.1 1.21 7 0 -1.9 3.61 8 1 -0.9 0.81 9 0 -1.9 3.61 10 2 0.1 0.01 Total 19 24.9 77 . 2 9 9 . 24 1 10 9 . 24 1 ) ( 1 2 2 = = - = - - = = n x x s n i i 3
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1 ) ( 1 1 2 2 2 - - = = = n n x x s n i n i i i i i x 2 i x 1 4 16 2 2 4 3 1 1 4 1 1 5 5 25 6 3 9 7 0 0 8 1 1 9 0 0 10 2 4 Total 19 61 77 . 2 9 9 . 24 9 10 361 61 1 10 10 ) 19 ( 61 1 ) ( 2 1 1 2 2 2 = = - = - - = - - = = = n n x x s n i n i i i This is the same answer – as we would expect. c. The standard deviation is
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solutions HMWK 1 - ISDS-361A & SD Panayiotis Skordi...

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