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If the mean and variance of six observations 7 , 10 , 11 , 15 , a , b are 10 and 20 3 , respectively, then the value of | a - b | is equal to:

Options

  1. A9
  2. B11
  3. C7
  4. D1

Correct answer

D. 1

Step-by-step solution

Given: Mean = 10 ⇒ 7 + 10 + 11 + 15 + a + b 6 = 10 ⇒ a + b = 17   … i And, Variance = 20 3 ⇒ 7 2 + 10 2 + 11 2 + 15 2 + a 2 + b 2 6 - 10 2 = 20 3 ⇒ 495 + a 2 + b 2 6 = 320 3 ⇒ 495 + a 2 + b 2 = 640 ⇒ a 2 + b 2 = 145       … ii Solve i and i i , we get a = 9 ,   b = 8 or a = 8 ,   b = 9 ∴ a - b = 1

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