Three observations of a random sample of size 5 are 12, 6, 15. If sample mean is 10 and difference between 2 missing observations is 1, the two missing observations are :

8, 9

The correct answer is Option (3) → 8, 9

Let the missing observation be x and y.

$x-y=1$   ....(1)

$\text{Mean} = \frac{\text{Sum of all observations}}{\text{Sample size}}$

$⇒10=\frac{12+6+15+x+y}{5}$

$⇒x+y=17$   ...(2)

Add (1) and (2)

$2x=18$

$x=9$ and $y=8$