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BITSAT2018MathematicsStatisticsActual

The arithmetic mean of a set of observation is X ¯ . If each observation is divided by α and increased by 10 , then the mean of the new series is

Options

  1. AX ¯ α
  2. BX ¯ + 10 α
  3. CX ¯ + 10 α α
  4. Dα X ¯ + 10

Correct answer

C. X ¯ + 10 α α

Step-by-step solution

Let x 1 ,   x 2 , … , x n be n observations. Then, X ¯ = 1 n Σ x i Let y i = x i α + 10 Then. 1 n ∑ i = 1 n y i = 1 α 1 n Σ x i + 1 n 10 n ⇒ X ¯ new = 1 α X ¯ + 10 = X ¯ + 10 α α Hence option (c) is correct.

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