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

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 \cdot y $ is equal to,

MARKS App · Accepted Answer

Mean = x - = 3 + 7 + 9 + 12 + 13 + 20 + x + y 8 = 10 ⇒ x + y = 16 … i Variance σ 2 = ∑ x i 2 8 - x - 2 = 25 9 + 49 + 81 + 144 + 169 + 400 + x 2 + y 2 8 - 100 = 25 ⇒ x 2 + y 2 = 148 … i i x + y 2 = 16 2 = x 2 + y 2 + 2 x y = 256 ⇒ x y = 54

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