If mean and variance of eight numbers 3,7,9,12,13,20, x and y be 10 and 25 respectively, then mathrm

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13.Statistics

hard

If the mean and variance of eight numbers $3,7,9,12,13,20, x$ and $y$ be $10$ and $25$ respectively, then $\mathrm{x} \cdot \mathrm{y}$ is equal to

A

$48$

B

$56$

C

$54$

D

$58$

(JEE MAIN-2020)

Solution

$\frac{3+7+9+12+13+20+x+y}{8}=10$

$x+y=16$

$\frac{\Sigma x^{2}}{n}-\left(\frac{\Sigma x}{n}\right)^{2}=25$

$3^{2}+7^{2}+9^{2}+12^{2}+13^{2}+20^{2}+\mathrm{x}^{2}+\mathrm{y}^{2}=1000$

$x^{2}+y^{2}=148$

$x y=54$

Standard 11

Mathematics

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