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Lecture 6 Dispersion

# Lecture 6 Dispersion - Dening Dispersion Quantitative data...

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Defining Dispersion Quantitative data 1) Difference between highest and lowest scores 2) The width of an interval spanning some pre-specified 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

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Range Defined 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

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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
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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

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Quartile Deviation Also called Semi-Interquartile 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 3 -Q 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

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