lecture_1_2 - Looking at data distributions Describing...

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    Looking at data: distributions Describing distributions with numbers IPS chapter 1.2 © 2006 W.H. Freeman and Company
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Objectives (IPS chapter 1.2) Describing distributions with numbers Measure of center: the mean Measure of center: the median Measure of spread: the quartiles Five-number summary and boxplot Measure of spread: the standard deviation Choosing among summary statistics Changing the unit of measurement
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The mean or arithmetic average To calculate the average, or mean, add all values, then divide by the number of individuals. It is the “center of mass.” Sum of heights is 1598.3 divided by 25 women = 63.9 inches 58.2 64.0 59.5 64.5 60.7 64.1 60.9 64.8 61.9 65.2 61.9 65.7 62.2 66.2 62.2 66.7 62.4 67.1 62.9 67.8 63.9 68.9 63.1 69.6 63.9 Measure of center: the  mean
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x = 1598 .3 25 = 63 .9 Mathematical notation: = = n i i x n x 1 1 w o ma n ( i ) h ei gh t ( x ) w o ma n ( i ) h ei gh t ( x ) i = 1 x 1 = 5 8 . 2 i = 14 x 14 = 6 4 . 0 i = 2 x 2 = 5 9 . 5 i = 15 x 15 = 6 4 . 5 i = 3 x 3 = 6 0 . 7 i = 16 x 16 = 6 4 . 1 i = 4 x 4 = 6 0 . 9 i = 17 x 17 = 6 4 . 8 i = 5 x 5 = 6 1 . 9 i = 18 x 18 = 6 5 . 2 i = 6 x 6 = 6 1 . 9 i = 19 x 19 = 6 5 . 7 i = 7 x 7 = 6 2 . 2 i = 20 x 20 = 6 6 . 2 i = 8 x 8 = 6 2 . 2 i = 21 x 21 = 6 6 . 7 i = 9 x 9 = 6 2 . 4 i = 22 x 22 = 6 7 . 1 i = 10 x 10 = 6 2 . 9 i = 23 x 23 = 6 7 . 8 i = 11 x 11 = 6 3 . 9 i = 24 x 24 = 6 8 . 9 i = 12 x 12 = 6 3 . 1 i = 25 x 25 = 6 9 . 6 i = 13 x 13 = 6 3 . 9 n = 2 5 Σ = 1 5 9 8 . 3 Learn right away how to get the mean using your calculators. n x x x x n + + + = ... 2 1
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Measure of center: the  median The median is the midpoint of a distribution—the number such that half of the observations are smaller and half are larger. 1. Sort observations by size. n = number of observations ______________________________ 1 1 0.6 2 2 1.2 3 3 1.6 4 4 1.9 5 5 1.5 6 6 2.1 7 7 2.3 8 8 2.3 9 9 2.5 10 10 2.8 11 11 2.9 12 3.3 13 3.4 14 1 3.6 15 2 3.7 16 3 3.8 17 4 3.9 18 5 4.1 19 6 4.2 20 7 4.5 21 8 4.7 22 9 4.9 23 10 5.3 24 11 5.6 n = 24 n /2 = 12 Median = (3.3+3.4) /2 = 3.35 2.b. If n is even, the median is the mean of the two middle observations.
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