Mean is dependent on both scale and shift factor hence scale and change of origin as :
Mean(ax + b) = a . Mean(x) + b
where a is the scale factor and b is the shift factor
Whereas standard deviation and variance depends on scale factor only.
S.D.(ax + b) = |a| . S.D(x) where S.D is the standard deviation
Var(ax + b) = a2 Var(x) where Var(x) is the variance
Hence the answer to the above question should be A) option as standard deviation depends on scale only.
X->YZ , Y->XZ , ...