Let observations are denoted by xi for 1≤i<2n. ∴Mean(x)=
∑xi
2n
=
(a+a+a+...+a)−(a+a+a+...+a)
2n
⇒x=0 and σx2=
∑x12
2n
−(x)2 =
⏞a2+a2+a2+....+a22n times
2n
−0=a2 ⇒σx2=a2⇒σx=a According to the question, adding a constant b, then new mean (y)=x+b=5 ⇒0+b=5 ⇒b=5 and new SD (σy)=σx ⇒σy=σx=20 ⇒a=20 ∴a2+b2=400+25=425