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The mean and variance of seven observations are 8 and 16 respectively. If five of the observations are 2 , 4 , 10 , 12 and 14 , then the remaining two observations are

Options

  1. A5 , 7
  2. B3 , 5
  3. C6 , 8
  4. D4 , 2

Correct answer

C. 6 , 8

Step-by-step solution

Let x and y be remaining 2 observations Mean = 8 = 2 + 4 + 10 + 12 + 14 + x + y 7 ⇒ x + y = 14 ...(i) Variance = 16 = 1 7 2 2 + 4 2 + 1 0 2 + 1 2 2 + x 2 + y 2 - 8 2 ⇒ x 2 + y 2 = 100 ...(ii) now solving equation (i) and (ii), we get, x = 8 , y = 6 or x = 6 , y = 8

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