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The variance of 50 observations is 7 . If each observation is multiplied by 6 and then 5 is subtracted from it, then the variance of the new data is

Options

  1. A37
  2. B42
  3. C247
  4. D252

Correct answer

D. 252

Step-by-step solution

Let the observations be x 1 ,   x 2 ,   x 3 , … , x 50 and the mean be x ¯ . From the given data, Variance = 7 , the number of observations n = 50 . Variance = 1 n ∑ x i - x ¯ 2 ⇒ 7 = 1 50 ∑ x i - x ¯ 2 ⇒ 350 = ∑ x i - x ¯ 2     . . . 1 Each observation is multiplied by 6 and then 5 is subtracted. Let the new observations be y 1 ,   y 2 ,   y 3 , … , y 50 . y i = 6 x i - 5 x i = y i + 5 6     . . . 2 The new varian

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