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JEE Main2018MathematicsStatisticsActual

If ∑ i = 1 9 x i − 5 = 9 and ∑ i = 1 9 x i − 5 2 = 45 , then the standard deviation of the 9 items x 1 , x 2 , … . , x 9 is

Options

  1. A3
  2. B9
  3. C4
  4. D2

Correct answer

D. 2

Step-by-step solution

Given ∑ i = 1 9 x i − 45 = 9 ⇒ ∑ i = 1 9 x i = 54 Also ∑ i = 1 9 x i 2 − 10 x i + 25 = 45 ⇒ ∑ i = 1 9 x i 2 − 10 × 54 + 25 × 9 = 45 ⇒ ∑ x i 2 = 45 + 540 − 225 = 360 ∴   σ 2 = ∑ x i 2 N − ∑ x i N 2 = 360 9 − ( 54 9 ) 2 So, variance = 40 − 36 = 4 ∴   S D = 2

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