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The mean and variance of $5$ observations are $5$ and $8$ respectively, if $3$ observations are $1,3,5$ respectively, then the cubic sum

of the remaining two observations is:
Option: 1
$1792$

Option: 2
$1216$

Option: 3
$1456$

Option: 4
$1072$

Answers (1)

best_answer

Let the observations are $1,2,3,\ a\ and\ b$

Mean, $M=\frac{9+a+b}{5}=5$

And, variance, $V=\frac{a^2+b^2+35}{5}-25\ =\ 8$

Or, $a+b=16$ and $a^2+b^2=130$

Therefore, $a=7\$ and $b=9$

Now, $a^2+b^2=7^{2}+9^{2}$

Or, $7^2+9^2=1072$

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