The mean and variance of 7 observations are 8 and 16, respectively. If five of the observations are 2, 4, 10, 12, 14. Find the remaining two observations.

Explanation

Mean `=bar{x}=frac{2+4+10+12+14+x+y}{7}=8`

`Rightarrow 56=42+x+y`

`Rightarrow x+y=14 quad ldots ldots .(1)`


Variance `=16=frac{1}{{n}} sum_{{i}=1}^{7}({x}_{{i}}-overline{{x}})^{2}`

`16=frac{1}{7}[(-6)^{2}+(-4)^{2}+(2)^{2}+(4)^{2}+(6)^{2}+{x}^{2}+{y}^{2}-2 times 8({x}+{y})+2 times(8)^{2}]` `16=frac{1}{7}[36+16+4+6+36+{x}^{2}+{y}^{2}-16(14)+2(64)] quad ldots ldots ldots .[{using}(1)]`

`16=frac{1}{7}[108+{x}^{2}+{y}^{2}-224+128]`

`16=frac{1}{7}[12+{x}^{2}+{y}^{2}]`

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