2018 · Q59
Let {-}{x₁ and {-}{x₂ (where {-}{x₂ > {-}{x₁) be the means of two sets comprising n₁ and n₂ (where n₂
Elementary MathematicsStatistics
- Ax1−\overset{-}{x_1}
- Bx−\overset{-}{x}
- Cx−\overset{-}{x}
- D(x1−−x−)\left(\overset{-}{x_1}-\overset{-}{x}\right)
Explanation
The combined mean x-bar = (n1 x-bar1 + n2 x-bar2)/(n1 + n2) is a weighted average of the two group means. A weighted average always lies strictly between the two values being averaged, so x-bar1 < x-bar < x-bar2 (given x-bar2 > x-bar1). This is option A.