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JEE Main20238 Apr 2023Morning ShiftMathematicsStatisticsActual

Let the mean and variance of 8 numbers x , y , 10 , 12 , 6 , 12 , 4 , 8 be 9 and 9 . 25 respectively. If x > y , then 3 x - 2 y is equal to _ _ _ _ _ _ _

Correct answer

0

Step-by-step solution

Given, the data x ,   y ,   10 ,   12 ,   4 ,   6 ,   8 ,   12 . So, Mean = x + y + 10 + 12 + 4 + 6 + 8 + 12 8 ⇒ 9 = x + y + 52 8 ⇒ x + y + 52 = 72 ⇒ x + y = 20 And, Variance = ∑ x i 2 n - ∑ x i n 2 ⇒ 9 . 25 = x 2 + y 2 + 100 + 144 + 16 + 36 + 64 + 144 8 - 9 2 ⇒ x 2 + y 2 = 218 ⇒ x + y 2 - 2 x y = 218 ⇒ 20 2 - 2 x y = 218 ⇒ 2 x y = 182 ⇒ x y = 91 Now solving x + y = 20   &   x y = 91 we get, x = 13 , &

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