Lecture05

# Lecture05 - Lecture 5 How much variety is there Measures of...

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1 Lecture 5 How much variety is there? Measures of variation Sociology 549 Paul von Hippel

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2 Measures of variation Sensitive (to extreme values) standard deviation (s) variance (s 2 ) range Robust interquartile range (IQR) Standard deviation is basis for standardization
3 Center vs. variation • Two distributions can have same center • But differ with respect to variation • 2 basketball teams Clippers Knicks • Similar mean height, between 6’6” and 6’7” • But they don’t match up well…

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4 Basketball teams: Mean heights Knicks Clippers Player Inches (Y) Player Inches (Y) 1Howard Eisley 74 Earl Boykins (now a Warrior) 65 2Charlie Ward 74 Keyon Dooling 75 3Mark Jackson 75 Jeff McInnis 76 4Larry Robinson 75 Quentin Richardson 78 5Latrell Sprewell 77 Corey Maggette 78 6Lavor Postell 77 Eric Piatkowski 78 7Allan Houston 78 Elton Brand 80 8Shandon Anderson 78 Harold Jamison 81 9Clarence Weatherspoon 79 Darius Miles 81 10Kurt Thomas 81 Obinna Ekezie 81 11Othella Harrington 81 Sean Rooks 82 12Marcus Camby 83 Lamar Odom 82 13Travis Knight 84 Michael Olowokandi 84 14Felton Spencer 84 Σ Y 1100 1021 n 14 13 Σ Y / n 78.6 78.54 Y
5 Variance and standard deviation • Most common measures are Variance (s 2 ) Standard deviation   (s) • To understand Must understand  deviation

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6 Deviations from the mean Deviation from the mean is Y is the value for a particular case Y =65 for Earl Boykins “Y bar” is the mean over all the cases Deviation= =-13.54 for Earl Boykins Interpretation: He is 13.54” shorter than the team mean Y Y - Clippers for the 54 . 78 = Y Y Y -
7 Variance: Calculation • Variance is the mean of the squared deviations. • Formula • Steps Calculate the deviation for each case Square each deviation Sum the squared deviation Divide by  N -1 (not  N ) Remember: N is sample size, # of cases • Why  N -1? If  N =1 you can’t see variation and you can’t divide by N -1=0 1 ) ( 2 2 - - = N Y Y S Y

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8 Variance: Example Clippers' Player Height Deviation Squared deviation 1 Earl Boykins 65 -13.54 183.29 2 Keyon Dooling 75 -3.54 12.52 3 Jeff McInnis 76 -2.54 6.44 4 Quentin Richardson 78 -0.54 0.29 5 Corey Maggette 78 -0.54 0.29 6 Eric Piatkowski 78 -0.54 0.29 7 Elton Brand 80 1.46 2.14 8 Harold Jamison 81 2.46 6.06 9 Darius Miles 81 2.46 6.06 10 Obinna Ekezie 81 2.46 6.06 11 Sean Rooks 82 3.46 11.98 12 Lamar Odom 82 3.46 11.98 13 Michael Olowokandi 84 5.46 29.83 Mean 78.54 Sum 277.23 N-1 12 Variance (s 2 ) 23.10 • Note influence of extreme cases (esp. Boykins)
9 Variance: Interpretation • More variety larger variance • Beyond that, not easy to interpret Variance is in squared units Need to un-square them

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10 Standard deviation: Calculation
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Lecture05 - Lecture 5 How much variety is there Measures of...

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