Mean and variance of 5 observations are 5 and 8 respectively. If 3 observations are 1,3,5 , then sum

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13.Statistics

hard

The mean and variance of $5$ observations are $5$ and $8$ respectively. If $3$ observations are $1,3,5$, then the sum of cubes of the remaining two observations is

A

$1072$

B

$1792$

C

$1216$

D

$1456$

(JEE MAIN-2023)

Solution

$\frac{1+3+5+a+b}{5}=5$

$a+b=16 \ldots \ldots(1)$

$\sigma^2=\frac{\sum x_1^2}{5}-\left(\frac{\sum x}{5}\right)^2$ $8=\frac{1^2+3^2+5^2+a^2+b^2}{5}-25$

$a^2+b^2=130 \ldots \ldots(2)$

$b y(1),(2)$

$a=7, b=9$

Standard 11

Mathematics

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