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NTA Abhyas JEE Main2020MathematicsStatisticsPractice

Let x 1 ,   x 2 ,   x 3 . . . . x k be k observations and w i = a x i + b for i = 1,   2 ,   3 . . . . . k , where a and b are constants. If mean of x i is 52 and their standard deviation is 12 and mean of w i is 60 and their standard deviation is 15 , then the value of a and b should be

Options

  1. Aa = 1.25 , b = - 5
  2. Ba = - 1.25 , b = 5
  3. Ca = 2.5 , b = - 5
  4. Da = 2.5 , b = 5

Correct answer

A. a = 1.25 , b = - 5

Step-by-step solution

w i = a x i + b ⇒ w ¯ = a x ¯ + b ⇒ 60 = a 52 + b …. (i) S . D   of   w = a S . D   of   x i 15 = a 1 2 ⇒ a = ± 1.25 …. (ii) From (i) and (ii), we get, If a = 1.25 ⇒ 60 = 65 + b ⇒ b = - 5 If a = - 1.25 ⇒ 60 = - 65 + b ⇒ b = 125

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