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Unformatted text preview: Defning Dispersion • Quantitative data • 1) DiFFerence between highest and lowest scores • 2) The width oF an interval spanning some prespecifed proportion oF scores • 3) The average amount by which scores deviate around some central point • 4) The magnitude oF dispersion expressed as a percentage oF the value oF the mean 1 Range • Defned as the diFFerence between the largest and smallest scores in the data set R = x (largest score) x (smallest score) 5 9 5 2 6 7 9 8 3 8 R = 9  2 = 7 2 Range: Pros and Cons • Pros: • Easy to compute and intuitive • Cons: • Uses information from only 2 scores • Overly sensitive to extreme scores • Not mathematically tractable • Tends to increase with sample size 3 Interquartile Range • A truncated range statistic spanning the middle 50% of scores in a distribution • Median  cuts off the lower 50% of the distribution from the upper 50% • First quartile  cuts off the lower 25% of the distribution from the upper 75% • Third quartile  cuts off the lower 75% of the distribution from the upper 25% 4 5 Interquartile Range • 1) Order observations from least to greatest • 2) Compute ( n +1)/4 , round to the nearest whole number and count in that many steps from both ends of the ordered data set • 3) Compute IQR = ( Q 3 Q 1 ), where Q 1 is the score corresponding to the 1st Quartile and Q 3 is the score corresponding to the 3rd Quartile . That is the Interquartile Range 6 Interquartile Range 2 3 5 5 6 7 8 8 9 9 ( n+ 1)/4 = (10+1)/4 = 2.75 ~ 3 IQR = Q 3 Q 1 = 8  5 = 3 7 Quartile Deviation • Also called SemiInterquartile Range • 1) Identify Q 1 and Q 3 as in IQR • 2) Compute QD = ( Q 3 Q 1 )/2 2 3 5 5 6 7 8 8 9 9 QD = (Q 3Q 1 )/2 = (8  5)/2 = 1.5 8 Interquartile Range/ Quartile Deviation • Pros: • Not affected by extreme scores or sample size • Interquartile Range commonly used for quantifying what counts as an outlier Mdn ± 2( IQR ) • Magnitude of Quartile Deviation roughly comparable to other common measures of quantitative dispersion 9 Interquartile Range/...
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This note was uploaded on 01/21/2009 for the course PSYC 60 taught by Professor Ard during the Winter '08 term at UCSD.
 Winter '08
 Ard

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