1.2 - Lookingatdata:distributions...

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  1 Looking at data: distributions Describing distributions with numbers
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The pattern of variation of a variable is called its distribution . The distribution of a quantitative variable records its numerical values and how often each value occurs. The shape and spread of a distribution can be displayed graphically (e.g., Histogram, Stemplot) or summarized by descriptive numerical values (e.g., mean, median, standard deviation, quartiles).
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Describing distributions with numbers Measures of center : mean, median Measures of spread : range, inter-quartile range, variance, standard deviation
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arithmetic average To calculate the average, or mean, add all values, then divide by the number of individuals. 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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Mathematical notation: = = n i i x n x 1 1 n x x x x n + + + = ... 2 1
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Mean is the “center of mass.” Balancing point
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The distribution of women’s heights appears symmetrical. The mean is a good numerical summary. 9 . 63 = x Height of 25 women in a class
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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. 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 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 25 12 6.1 n = 25 ( n +1)/2 = 26/2 = 13 Median = 3.4 2.a. If n is odd, the median is observation ( n
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This note was uploaded on 09/04/2010 for the course STAT 131 taught by Professor Isber during the Spring '08 term at University of California, Berkeley.

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1.2 - Lookingatdata:distributions...

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