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Standard XII

Mathematics

Standard Deviation about Mean

If the mean a...

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

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Solution

Mean $= \frac{64 + x + y}{8} = 10$
$\Rightarrow x + y = 16$

Variance $= \frac{\sum x_{i}^{2}}{n} - (¯ ¯ ¯ x)^{2}$
$\Rightarrow 25 = \frac{3^{2} + 7^{2} + 9^{2} + 12^{2} + 13^{2} + 20^{2} + x^{2} + y^{2}}{8} - 100 \Rightarrow 1000 = 852 + x^{2} + y^{2} \Rightarrow x^{2} + y^{2} = 148 \Rightarrow (x + y)^{2} - 2 x y = 148 \Rightarrow 256 - 2 x y = 148 ∴ x y = 54$

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Standard Deviation about Mean

Standard XII Mathematics

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

Mean =64+x+y8=10 ⇒x+y=16 Variance =∑x2in−(¯¯¯x)2 ⇒25=32+72+92+122+132+202+x2+y28−100⇒1000=852+x2+y2⇒x2+y2=148⇒(x+y)2−2xy=148⇒256−2xy=148∴xy=54

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