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NTA Abhyas JEE Main2020MathematicsStatisticsPractice

The mean and variance of 20 observations are found to be 10 and 4 respectively. On rechecking, it was found that an observation 8 is incorrect. If the wrong observation is omitted, then the correct variance is

Options

  1. A7
  2. B100 19
  3. C1400 361
  4. D1440 361

Correct answer

D. 1440 361

Step-by-step solution

We have n = 20 , x ¯ o l d = 10 , V a r o l d = 4 ⇒ x ¯ = Σ x i 20 ⇒ Σ x i = 20 0 ⇒ Σ x i n e w = 192, X ¯ n e w = 192 9 V a r o l d = Σ x i 2 20 - x ¯ o l d 2 4 = Σ x i 2 20 - 10 0 Σ x i 2 o l d = 208 0 Σ x i 2 n e w = 2080 - 64 = 201 6 V a r n e w = 2016 19 - 192 19 2 = 1440 361

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