transformations.pdf - Transformations Exercise CMSC320 Consider data for variable x = x1 x2 xn We use x to denote the sample mean of x and sx is the

transformations.pdf - Transformations Exercise CMSC320...

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Transformations Exercise CMSC320 Consider data for variable x = x 1 , x 2 , . . . , x n . We use x to denote the sample mean of x , and s x is the sample standard deviation of x . Part I For each of the following three transformations derive (a) the sample mean z , and (b) the sample standard deviation s z . 1. Centering z i = ( x i - x ) 2. Scaling z i = x i s x 3. Centering and scaling (standardizing) z i = ( x i - x ) s x Part II 4.Consider transformationzi= logxi. Show that the sample meanzequals the logarithm of the
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