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The mean and variance of 10 observations are found to be 10 and 4 respectively. On rechecking it was found that an observation 8 was incorrect. If it is replaced by 18 , then the correct variance is

Options

  1. A7
  2. B8
  3. C9
  4. D55 6

Correct answer

C. 9

Step-by-step solution

x ¯ o l d = 10 = Σ x i 10 ⇒ Σ x i o l d = 10 0 Σ x i n e w = 100 - 8 + 18 = 11 0 x ¯ n e w = 110 10 = 1 1 V a r o l d = 4 = Σ x i o l d 2 10 - x ¯ o l d 2 Σ x i o l d 2 = 104 0 Σ x i n e w 2 = 1040 - 64 + 32 4 = 130 0 V a r n e w = 1300 10 - 11 2 = 130 - 121 = 9

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