Question

The mean and variance of 7 observations are 8 and $16,$ respectively. If five observations are $2,4,10,12,14,$ then the absolute difference of the remaining two observations is :

• A. 2
• B. 4
• C. 3
• D. 1

Answer 1

The Correct Option is A

$\bar{x}=\frac{2+4+10+12+14+x+y}{7}=8$ $x+y=14\dots$ (i) $(\sigma)^{2}=\frac{\sum\left( x _{ i }\right)^{2}}{ n }-\left(\frac{\sum x _{ i }}{ n }\right)^{2}$ $16=\frac{4+16+100+144+196+ x ^{2}+ y ^{2}}{7}-8^{2}$ $16+64=\frac{460+x^{2}+y^{2}}{7}$ $560=460+x^{2}+y^{2}$ $x^{2}+y^{2}=100\dots$(ii) Clearly by (i) and (ii), $|x-y|=2$