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JEE Main202127 Jul 2021Evening ShiftMathematicsStatisticsActual

Let the mean and variance of the frequency distribution x : x 1 = 2 x 2 = 6 x 3 = 8 x 4 = 9 f : 4 4 α β be 6 and 6 . 8 respectively. If x 3 is changed from 8 to 7 , then the mean for the new data will be:

Options

  1. A4
  2. B5
  3. C17 3
  4. D16 3

Correct answer

C. 17 3

Step-by-step solution

Given x : x 1 = 2 x 2 = 6 x 3 = 8 x 4 = 9 Total f : 4 4 α β 8 + α + β f x : 8 24 8 α 9 β 32 + 8 α + 9 β f x - x 2 : 64 0 4 α 9 β 64 + 4 α + 9 β x = ∑ i = 1 4 f i x i ∑ i = 1 4 f i 32 + 8 α + 9 β = 8 + α + β × 6 ⇒ 2 α + 3 β = 16               . . . 1 Also, for the variance, σ 2 = ∑ f i x i - x 2   i = 1               &#1

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