The trade that dragged your average down

Question

Your first 9 trades average \80 of profit each. After a 10th trade, your average drops to \75. Solve in your head. How much did the 10th trade make? Aim: under 15 seconds.

Accepted Answer

Fast route, think in deviations from the new average of \75. The old 9 trades each sit \5 above the new average, a total surplus of 9 	imes 5 = \45. The 10th trade has to cancel that surplus and still hit the average, so it lands \45 below it: 75 - 45 = \30. Slow route for contrast: totals give 10 	imes 75 - 9 	imes 80 = 750 - 720 = 30. Same answer, bigger multiplications. Takeaway. "New item = new average + (old count) 	imes (change in average)." Here the change is -\5, so 75 + 9(-5) = \30. When the average drops, the new value sits below it by the whole accumulated surplus.

The trade that dragged your average down

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