chapter2

# 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
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
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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