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Manipal MET2010MathematicsStatistics

If x ₁ and x ₂ are the means of two distributions such that x ₁ x ₂ and x is the mean of the combined distribution, then

Options

  1. Ax x ₁
  2. Bx x ₂
  3. Cx = x ₁+ x ₂ 2
  4. Dx ₁ x x ₂

Correct answer

D. x ₁ x x ₂

Step-by-step solution

Let n₁ and n₂ be the number of observations in two groups having means X₁ and X₂ respectively. Then X = n₁ X ₁+n₂ X ₂ n₁+n₂ - X ₂ Now, X - X ₁= n₁ X ₁+n₂ X ₂ n₁+n₂ - X ₁= n₂ ( X ₂- X ₁ ) n₁+n₂ 0 [ X ₂ X ₁ ] X X ₁...(i) And X - X ₂= n ( X ₁- X ₂ ) n₁+n₂ 0 [ X ₂ X ₁ ] X X ₂...(ii) From Eqs. (i) and (ii), X ₁ X X ₂

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