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  • Mean and variance of 7 observation is 8 and 16. If 5 observations are 2,4,10,12,14 product of 2 observation is ?Option: 1

Mean and variance of 7 observation is 8 and 16. If 5 observations are 2,4,10,12,14 product of 2 observation is ?

Option: 1

24


Option: 2

96


Option: 3

54


Option: 4

48


Answers (1)

best_answer

Let the two observation is x and y

The observation are 2,4,10,12,14, x,y

\\\text { Mean }=\bar{x}=\frac{2+4+10+12+14+x+y}{7}=8 \\ \Rightarrow 56=42+x+y \\ \Rightarrow x+y=14 \quad\quad\quad\quad\quad\quad\quad\quad\quad\ldots \text { (i)}

\text { Variance }=16=\frac{1}{n} \sum_{i=l}^{7}\left(x_{i}-\bar{x}\right)^{2}

\\ 16=\frac{1}{7}\left[(-6)^{2}+(-4)^{2}+(2)^{2}+(4)^{2}+(6)^{2}+x^{2}+y^{2}-2 \times 8(x+y)+2 \times(8)^{2}\right] \\ 16=\frac{1}{7}\left[36+16+4+6+36+x^{2}+y^{2}-16(14)+2(64)\right]\;\;\;\;[ \operatorname{using}\;\;(\text{i})] \\ 16=\frac{1}{7}\left[108+x^{2}+y^{2}-224+128\right] \\ 16=\frac{1}{7}\left[12+x^{2}+y^{2}\right] \\ \Rightarrow x^{2}+y^{2}=112-12=100 \\ x^{2}+y^{2}=100 \quad \ldots \ldots\text{(ii)}from (i) and (ii)

\\(x+y)^2=196\\x^2+y^2+2xy=196\\\Rightarrow 100+2xy=196\\\Rightarrow 2xy=96\\xy=48

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Anam Khan

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