Blending two desks' averages

Question

Desk A has 20 traders averaging a \75k bonus. Desk B has 30 traders averaging a \85k bonus. Solve in your head. What is the combined average bonus across all 50 traders? Aim: under 15 seconds.

Accepted Answer

The combined figure is a weighted average, so it must land between 75 and 85, pulled toward the larger desk (B). Fast route, deviations from a round guess of \80k: - Desk A: 20 traders at -\5k each = -\100k. - Desk B: 30 traders at +\5k each = +\150k. Net +\50k spread over 50 traders is +\1k, so the combined average is 80 + 1 = \81k. Slow route for contrast: \dfrac{20(75) + 30(85)}{50} = \dfrac{1500 + 2550}{50} = \dfrac{4050}{50} = 81. Same answer. Takeaway. A blended average sits between the two group averages, closer to the bigger group. Picking a convenient anchor (here \80k) and summing w…

Blending two desks' averages

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