The mean and variance of 8 observations are 10 and 13.5 respectively. If 6 of these observations are 5, 7, 10, 12, 14, 15, then the absolute difference of the remaining two observations is

Let the remaining two observations be x and y. Then,Mean =10⇒ 18(5+7+10+12+14+15+x+y)=10⇒ 63+x+y=80⇒x+y=17Variance =13.5⇒ 1825+49+100+144+196+225+x2+y2−102=13.5⇒ x2+y2+739=908⇒ x2+y2=169∴    (x−y)2+(x+y)2=2x2+y2⇒    (x−y)2=2×169−289=49⇒    |x−y|=7