Unformatted text preview: 8 s In general, if x 1 ,...,x n are observations from a variable X , and x 1 ,...,x n are the linearly transformed data points: x i = ax i + b, i = 1 ,...,n then ¯ x = a ¯ x + b, ( s ) 2 = a 2 s 2 , s =  a  s Note: In the case of nonlinear transformations (e.g. X = √ X , X = e X , etc.), the previous property does not hold. A logarithmic transformation of a variable X is a new variable of the form: Y = ln( X ) Consider the logarithmic measurements y i = ln( x i ) ,i = 1 ,...,n . The geometric mean of the sample x 1 ,...,x n is deﬁned by: g = e ¯ y , where ¯ y = 1 n n X i =1 y i . The geometric standard deviation of the sample x 1 ,...,x n is deﬁned by: e s y , where s y = v u u t 1 n1 n X i =1 ( y i¯ y ) 2 ....
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 Fall '13
 Statistics, Biostatistics, Standard Deviation, Sample standard deviation, linear transformation, new variable

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