Chapter02

The Basic Practice of Statistics (Paper) & Student CD

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Numerical descriptors BPS chapter 2 © 2006 W.H. Freeman and Company
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Objectives (BPS 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 Choosing among summary statistics Using technology Organizing a statistical problem
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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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n n x .... x x x 2 1 + + + = x = 1598.3 25 = 63.9 Mathematical notation: x = 1 n i x i = 1 n " 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 = 2 5 Σ = 1 5 9 8 . 3 Learn right away how to get the mean using your calculators.
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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 symmetrical. The mean is a good numerical summary. 3 . 69 = x Height of 25 women in a class
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Height of plants by color 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 . 63 = x 5 . 70 = x 3 . 78 = x
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Apply your knowledge Go to page 39 and work on the following problem: 2.1 Pulling wood apart
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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.
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Chapter02 - Numerical descriptors BPS chapter 2 2006 W.H...

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