Introduction to statistics

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Question

If the mean and variance of eight numbers 3,7,9,12,13,20, x and y be 10 and 25 respectively, then x.y is equal to ________

Easy

Solution

$\frac{3 + 7 + 9 + 12 + 13 + 20 + x + y}{8} = 10$
$x + y = 16$
$\frac{\sum x^{2}}{n} - {(\frac{\sum x}{n})}^{2} = 25$
$3^{2} + 7^{2} + 9^{2} + 12^{2} + 13^{2} + 20^{2} + x^{2} + y^{2} = 1000$
$x^{2} + y^{2} = 148$
$x y = 54$

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