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BITSAT2024MathematicsStatisticsActual

The variance of 20 observations is 5 . If each observation is multiplied by 2 , then the new variance of the resulting observation is

Options

  1. A2^3 5
  2. B2^2 5
  3. C2 5
  4. D2^4 5

Correct answer

B. 2^2 5

Step-by-step solution

Let the observations be x₁, x₂, , x₂₀ and x be their mean. Given that, variance =5 and n= 20. We know that, Variance ( ^2 )= 1 n _ i=1 ²⁰ (x_i- x )^2 i.e. 5= 1 20 _ i=1 ²⁰ (x_i- x )^2 or _ i=1 ²⁰ (x_i- x )^2=100 .....(i) If each observation is multiplied by 2 and the new resulting observations are y_i , then y_i=2 x_i i.e., x_i= 1 2 y_i Therefore, y = 1 n _ i =1 ²⁰ y _ i = 1 20 _ i =1 ²⁰ 2 x _ i =2 1 20 _ i =1 ²⁰ x _ i i.e., y =2 x or x = 1 2 y . On substituting the values of x_i and x in eq. (i), we get _ i=1 ²⁰ (

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