Honestly, the notation of the problem is unclear to me. Your definitions of mean and variance look like they should include a sum -- is that what Pkm is?
suppose we have a problem like this
Properties
A B C D E F G
1 AA1 1.8 2.5 3.8 1.9 -3.5 -3.5 -3.2
2 AA2 2.95 1.69 -0.83 -2.52 -0.33 1.61 2.19
3 AA3 4.12 5.2 -1.65 -0.48 1.39 -1.24 3.25
4 AA4 0.6 -1.19 -1.2 -0.25 -0.62 1.21 2.06
5 AA5 1.73 1.14 1.19 1.56 1.16 1.41 1.58
6 AA6 1.9 1.8 1.95 2 1.55 1.75 2.1
7 AA7 1.75 -1.27 -1.66 0.03 -1.5 0.51 1.55
Then the value of each property Pkm (k=1...7,m=1....7)
where k ---> AA1.......AA7
m----> A....G
so
P1 =( Pkm - Uk/Sk )
Where Uk defined as mean of property k and is equal to 1\7 * Pkm
and Sk is defined as variance of property k and is eaual to 1/6(Pkm-Uk)2
So we want to calculate P1 so how to proceed with this problem??
Here defintion of Pkm is just like normal X value when used in calculating mean
Uk = 1/N X
where Uk is mean and X is just same as Pkm.
Here we are referring to the above mentioned question where X or Pkm can be defined ..
K=1...7 or AA1....AA7
m=1...7 or A.....G
So it is needed to calculate mean and variance ....