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lecture5 - Variability(Chapter 4 Types of measures...

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Variability (Chapter 4) Types of measures Computing measures Choosing you measure 0 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 0 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 all 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 wouldn t help you out much in deciding how long you should wait This is where variability comes in
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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
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The distance between the lower real limit of the minimum score and the upper real limit of the maximum score 0 1 2 3 1 2 3 4 5 6 7 8 9 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
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IQR: Distance between the 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).
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