Lecture 6 Notes[1]

Lecture 6 Notes[1] - STAT 225 Lecture 6 Notes Variance,...

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STAT 225 Lecture 6 Notes Variance, Covariance, Correlation Def n :The population variance denoted by 2 is a measure of how spread out a population is about the population mean μ. Def n : The population standard deviation, σ, is the positive square root of the population variance. Def n : Sample v ariance : s 2 , average (almost) of the square of deviations of observations from the mean. This statistic provides a measure of spread about the center of a distribution. Again, in most practical situations this statistic provides the best possible estimate for the population variance 2 . s 2 = 2 1 () 1 n i i XX n Def n : Standard Deviation : s , square root of the sample variance, common way for measuring how far observations are from the mean. Ex. Calculate the sample variances and standard deviations for the two variables below. X Y -4 -5 -2 0 2 5 4 10 2 X s = 2 Y s = X s = Y s =

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Def n : The sample covariance is a measure of how two quantitative variables vary together. This statistic applies when the variables are measured together in pairs, i.e. the data look like: 1 {( , )} n j j j xy 1 ( )( ) 1 n jj j XY X X Y Y S n  Remark: Notice how the sample variance is just a special case of the sample covariance.
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This note was uploaded on 05/19/2011 for the course STAT 225 taught by Professor Martin during the Spring '08 term at Purdue.

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Lecture 6 Notes[1] - STAT 225 Lecture 6 Notes Variance,...

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