Explanation
CONCEPT:
Mean is represented as x=n∑i=1nxi.
Mean deviation for ungrouped data: For n observation x1, x2, … , xn, the mean deviation about their mean x is given by M.D(x)=n∣xi−x∣.
Mean deviation about their median M is given by M.D(M)=n∣xi−M∣.
CALCULATIONS:
It is given that wi=pxi+ k
X=48,σX=12
W=55,σW=15
Now as given wi=pxi+k
∴W=pX+k
⇒55=48p+k
⇒Var(w)=Var(px+k)
⇒Var(w)=p2Var(x)
As a variance of constants are zero.
σw2=p2(σX2)
⇒152=p2(122)
⇒p2=144225
=p=1215=45
Now putting the value of p in the equation 55=48p+k
⇒55=48(45)+k
⇒k=5
So, p= 1. 25 and k= - 5
Therefore option (1) is the correct answer.
