# 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: Option: 1 9 Option: 2 5 Option: 3 3 Option: 4 7

$\\\overline{\mathrm{x}}=10\\ \Rightarrow \bar{x}=\frac{63+a+b}{8}=10 \\\Rightarrow a+b=17\;\;\;\;\;\;\;\;\;\;\;\;\ldots(1) \\\text{Since, variance is independent of origin. So, we subtract 10 from each observation. So,} \\\sigma^{2}=13.5=\frac{79+(a-10)^{2}+(b-10)^{2}}{8}-(10-10)^{2} \\\Rightarrow a^{2}+b^{2}-20(a+b)=-171\\ \Rightarrow a^{2}+b^{2}=169\;\;\;\;\;\;\;\;\;\;\;\;\ldots(2)\\ \text{From } (1)\; \& \;(2);\\ a =12\; and \;b=5$

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