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JEE Main202226 Jun 2022Evening ShiftMathematicsStatisticsActual

Let the mean of 50 observations is 15 and the standard deviation is 2 . However, one observation was wrongly recorded. The sum of the correct and incorrect observations is 70 . If the mean of the correct set of observations is 16 , then the variance of the correct set is equal to

Options

  1. A10
  2. B36
  3. C43
  4. D60

Correct answer

C. 43

Step-by-step solution

By using the formula of mean we get, = ∑ x i 50 = 15 ⇒ ∑ x i = 750 Now variance = ∑ x i 2 50 - 15 2 = 2 2 ⇒ ∑ x i 2 = 11450 ⇒ ∑ x i new = 50 × 16 = 800 So, ∑ x i new - ∑ x i = 800 - 750 = 50 Hence, if wrong observation was x then corrected one is x + 50 . ⇒ x + x + 50 = 70 ⇒ x = 10 Therefore, the correct observation = 60 . Now, ∑ x i 2 new = 11450 - 10 2 + 60 2 = 14950 Therefore, variance of the correct set = 14950 50 - 16 2 = 299 -

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