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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)

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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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