chapter2 - Numericaldescriptors PSLS chapter 2 2009 W.H....

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    Numerical descriptors PSLS chapter 2 © 2009 W.H. Freeman and Company
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Objectives (PSLS chapter 2) Describing distributions with numbers Measure of center: mean and median Measure of spread: quartiles and standard deviation The five-number summary and boxplots IQR and outliers Dealing with outliers Choosing among summary statistics Organizing a statistical problem
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The mean or arithmetic average To calculate the average (mean) of a data set, add all values, then divide by the number of individuals. It is the “center of mass.” Measure of center: the mean n n x .... x x x 2 1 + + + = x = 1 n i x i = 1 n Learn right away how to get the mean using your calculators.
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x = 159 8 .3 25 = 63 .9 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 Heights (inches) of 25 women
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Your numerical summary must be meaningful Here the shape of the distribution is wildly irregular. Why? Could we have more than one plant species or phenotype? 6 . 69 = x The distribution of women’s height appears coherent and symmetric. The mean is a good numerical summary. 9 . 63 = x Height of 25 women in a class
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0 1 2 3 4 5 Height in centimeters Number of plants red pink blue 58 60 62 64 66 68 70 72 74 76 78 80 82 84 A single numerical summary here would not make sense. 9
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chapter2 - Numericaldescriptors PSLS chapter 2 2009 W.H....

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