Week 2 -- Variability

Week 2 -- Variability - NUMERICAL DESCRIPTIVE STATISTICS...

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NUMERICAL NUMERICAL DESCRIPTIVE STATISTICS DESCRIPTIVE STATISTICS Measures of Variability Measures of Variability
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Another Description of the Data -- Variability For Data Set A below, the mean of the 10 observations is 2.60. SET A: 4,2,3,3,2,2,1,4,3,2 But each of the following two data sets with 10 observations also has a mean of 2.60 SET B: 2,2,2,2,3,3,3,3,3,3 SET C: 0,0,1,1,4,4,4,4,4,4 Although sets A, B, and C all have the same mean, the “spread” of the data differs from set to set.
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The “Spread” of the Data Grades 0 1 2 3 4 5 0 1 2 3 4 Data Set A Grades 0 2 4 6 8 0 1 2 3 4 Data Set B Grades 0 2 4 6 8 0 1 2 3 4 Data Set C Most “spread” Least “spread”
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Numerical Data Numerical Data Properties Mean Median Mode Central Tendency Range Variance Standard Deviation Variation Percentiles Relative Standing Interquartile Range Z–scores
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Measures of Variability Population Variance σ 2 ; Standard Deviation σ Sample Range Variance s 2 ; Standard Deviation s
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The Range When we are talking about a sample, the range is the difference between the highest and lowest observation In the sample there were some A’s (4’s), and the lowest value in the sample was a D (1) Sample range = 4 - 1 = 3
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Range 1. Measure of dispersion 2. Difference between largest & smallest observations Range = X largest – X smallest 3. Ignores how data are distributed 7 7 8 8 9 9 10 10 7 7 8 8 9 9 10 10 Range = 10 – 7 = 3 Range = 10 – 7 = 3
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Another Approach to Variability The range only takes into account the two most extreme values A better approach Look at the variability of all the data In some sense find the “average” deviation from the mean The value of an observation minus the mean can be positive or negative The plusses and minuses cancel each other out giving an average value of 0 Need another measure
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Week 2 -- Variability - NUMERICAL DESCRIPTIVE STATISTICS...

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