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Unformatted text preview: Variability (Chapter 4) Types of measures Computing measures Choosing you measure 11.25 22.50 33.75 45.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Frequency Score 10 20 30 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Frequency Score M=6 for both distributions. Would it be fair to say they were the same? The Three Stooges, characters, and al related indicia are trademarks of C3 Entertainment, Inc. On 5 different occasions Moe: 30 min. late every time Curly: 25, 35, 28, 32, 30 min. late Larry: On time, 60, 30 min early, 90 min late, 30 min late All average 30 min. late The point: if you were waiting for one of them, the average wouldnt help you out much in deciding how long you should wait This is where variability comes in Is a quantitative measure of the amount of spread of the scores in a distribution. Provides a measure of consistency within a distribution Can be used to determine how well a single score (or set) represents the distribution Can be used to estimate how well a sample characterizes a population The distance between the lower real limit of the minimum score and the upper real limit of the maximum score 1 2 3 123456789 scores frequency RANGE Not the range How to get it: 1.Get the largest score (X max ) 2.Get the smallest score (X min ) 3.Get real limits for X max and X min 4.Range = X maxURL X minLRL Example: Scores: 5, 7, 9, 12, 16 X maxURL = 16.5 X minLRL= 4.5 Range = 16.5  4.5 = 12 IQR: Distance between the f rst and third quartile. First Quartile: Score that separates the lowest 25 % percent of the scores (25 percentile). Third Quartile: Score that separates the lowest 75 % percent of the scores (75 percentile). IQR = Q3  Q1 IQR = Q3  Q1 = 5.5  3.5 = 2.0 Q3 Q1 Note use of URL for both Q3 and Q1 IQR = Q3  Q1 = Q3  3.5 = ? Use interpolation to find Q3 Q3=75% 4.5 = upper real limit of 50th4....
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 Fall '08
 COLLINS

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