Question

The Mean and variance of 7 observations are 8 and 16 respectively. If 5 observations are 2,4,10,12,14 find the remaining two observations

• A. 3,4
• B. 6,8
• C. 5,13
• D. 3,8

Answer 1

The correct option is B 6,8

Mean = 8 $\Rightarrow$ x + y = 14 (assume unknown observations as x & y)
Variance $=16\Rightarrow x^2+y^2=100$
$\therefore (x+y{)}^2+(x-y{)}^2=2(x^2+y^2)$
$\Rightarrow (x-y{)}^2=4\Rightarrow x-y=\pm 2$
$\therefore onsolvingx+y=14andx-y=\pm 2,wehave$
$x=6,y=8\left(or\right)x=8,y=6$