Given, data ={6,10,7,13,a,12,b,12} Mean =9, Variance =
37
4
Now, mean =
∑
xi
n
=
6+10+7+13+a+12+b+12
8
or 9=
60+a+b
8
⇒72=60+a+b ⇒a+b=12 . . . (i) Variance =
∑xi2
n
−Σ(
xi
n
)2
37
4
=
62+102+72+132+a2+122+b2+122
8
⇒
37
4
=
642+a2+b2
8
−81 ⇒
37
4
=
642+a2+b2−648
8
⇒74=a2+b2−6 ⇒a2+b2=80 . . . (ii) ⇒(a+b)2=a2+b2+2ab Putting the values from Eqs. (i) and (ii), we get 2ab=(a+b)2−(a2+b2) ⇒2ab=122−80=64 Now, (a−b)2=a2+b2−2ab =80−64=16