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The mean and variance of 20 observations are found to be 10 and 4 , respectively. On rechecking, it was found that an observation 9 was incorrect and the correct observation was 11, then the correct variance is

Options

  1. A3.99
  2. B4.01
  3. C4.02
  4. D3.98

Correct answer

A. 3.99

Step-by-step solution

∑ x i 20 = 10         …   ( i ) ∑ x i 2 20 - 100 = 4             …   ( i i ) ∑ x i 2 = 104 × 20 = 2080 Actual mean = 200 - 9 + 11 20 = 202 20 Variance = 2080 - 81 + 121 20 - 202 20 2 = 2120 20 - 10.1 2 = 106 - 102.01 = 3.99

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