chap03-a3 - Statistics: Chapter 3 Describing Data Using...

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Chap 3-1 Statistics: Chapter 3 Describing Data Using Numerical Measures
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Chap 3-2 After completing this chapter, you should be able to: Compute and interpret the mean, median, and mode for a set of data Compute the range, variance, and standard deviation and know what these values mean Construct and interpret a box and whisker graph Compute and explain the coefficient of variation and z scores Use numerical measures along with graphs, charts, and tables to describe data Chapter Goals
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Chap 3-3 Chapter Topics Measures of Center and Location Mean, median, mode Other measures of Location Weighted mean, percentiles, quartiles Measures of Variation Range, interquartile range, variance and standard deviation, coefficient of variation Using the mean and standard deviation together Coefficient of variation, z-scores
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Chap 3-4 Summary Measures Center and Location Mean Median Mode Other Measures of Location Weighted Mean Describing Data Numerically Variation Variance Standard Deviation Coefficient of Variation Range Percentiles Interquartile Range Quartiles
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Chap 3-5
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Chap 3-6 Notation
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Chap 3-7 Measures of Center and Location Center and Location Mean Median Mode Weighted Mean N x n x x N i i n i i = = = μ = 1 1 = μ = i i i W i i i W w x w w x w X Overview
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Chap 3-8 Mean (Arithmetic Average) The Mean is the arithmetic average of data values Population mean Sample mean n = Sample Size N = Population Size n x x x n x x n n i i + + + = = = 2 1 1 N x x x N x N N i i + + + = = μ = 2 1 1
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Chap 3-9 Mean (Arithmetic Average) The most common measure of central tendency Mean = sum of values divided by the number of values Affected by extreme values (outliers) (continued) 0 1 2 3 4 5 6 7 8 9 10 Mean = 3 0 1 2 3 4 5 6 7 8 9 10 Mean = 4 3 5 15 5 5 4 3 2 1 = = + + + + 4 5 20 5 10 4 3 2 1 = = + + + +
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Chap 3-10 Median In an ordered array, the median is the “middle” number, i.e., the number that splits the distribution in half The median is not affected by extreme values 0 1 2 3 4 5 6 7 8 9 10 Median = 3 0 1 2 3 4 5 6 7 8 9 10 Median = 3
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Chap 3-11 Median To find the median, sort the n data values from low to high (sorted data is called a data array ) Find the value in the i = (1/2)n position The i th position is called the Median Index Point If i is not an integer, round up to next highest integer (continued)
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Chap 3-12 Median Example Note that n = 13 Find the i = (1/2)n position: i = (1/2)(13) = 6.5 Since 6.5 is not an integer, round up to 7 The median is the value in the 7th position : M d = 12 (continued) Data array: 4, 4, 5, 5, 9, 11, 12, 14, 16, 19, 22, 23, 24
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Chap 3-13 Mode A measure of location The value that occurs most often Not affected by extreme values Used for either numerical or categorical data There may be no mode There may be several modes 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Mode = 5 0 1 2 3 4 5 6 No Mode
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This note was uploaded on 02/23/2011 for the course OM 300 taught by Professor Bobsanders during the Spring '11 term at Essex County College.

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chap03-a3 - Statistics: Chapter 3 Describing Data Using...

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