Chpt 4 - Variability Chapter 4 Variability Measure of the degree to which the scores in a distribution are spread out or clustered together

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Gibney PSY230 Chapter 4 Variability 1 Chapter 4 Variability Variability • Measure of the degree to which the scores in a distribution are spread out or clustered togethe clustered together • Helps describe the distribution • Measure of how well an individual score represents the distribution Symmetrical distributions with different variability Three measures of variability • Range • Standard deviation Vi • Variance The Range • The distance covered by the scores in a distribution •Completely determined by two extreme scores • Highest – lowest score = range • Considered a crude, unreliable measure of variability Standard Deviation • Uses the mean as a reference • Measures variability by looking at how far hi f t h each score is from the mean • Average distance from the mean • Concept is simple formulas look scary
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Gibney PSY230 Chapter 4 Variability 2 Deviation is the distance from the mean Each score in a distribution has a corresponding deviation score Deviation score = X - μ (score - mu) Examples • In a distribution where μ = 30, and X = 35 then the deviation would be X- μ or 35-30 or 5 • In the same distribution where μ = 30 and X=25 the deviation would be X- μ or 25-30 or -5 • Note that the deviation score has 2 parts a sign (+/-) and a size • In this case the first score (35) is 5 units above the mean and the second score (25) is 5 units below the mean Logic • If you want to find the AVERAGE distance of each score from the mean it is only logical to calculate the mean of the deviation scores • Easy to do • Except. . . Average Deviation Calculation X X- μ 8 3 1. Find the mean X/n 2. Subtract the mean from each score (deviation) 1 0 X- μ 3. Find the average deviation (X- μ )/n Variance • Cannot just calculate average distance from the mean • By definition it always has to add up to zero • It is balanced • Solution is to square each deviation score to get rid of negative signs • This results in a score called the variance • Mean squared deviation is called the variance Standard Deviation • Variance is ok but not exactly what we had in mind as a measure • In order to correct for squaring the numbers the last stem in computing the standard deviation is to take the square root of the variance Variance Deviation Standard =
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This note was uploaded on 01/05/2011 for the course PSYC 230 taught by Professor Delaney during the Spring '08 term at University of Arizona- Tucson.

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Chpt 4 - Variability Chapter 4 Variability Measure of the degree to which the scores in a distribution are spread out or clustered together

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