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
