The eighth trade that moved your average

Question

Your first 7 trades average \46 of profit each. After an 8th trade, your average is \52. Solve in your head. How much did the 8th trade make? Aim: under 15 seconds.

Accepted Answer

Fast route, think in deviations from the new average. The old 7 trades each sit \6 below the new average of \52, a total deficit of 7 	imes 6 = \42. The 8th trade must cover that deficit and hit the average itself: 52 + 42 = \94. Slow route for contrast: totals give 8 	imes 52 - 7 	imes 46 = 416 - 322 = 94. Same answer, bigger numbers. Takeaway. "New item = new average + (old count) × (change in average)." Here: 52 + 7 	imes 6 = 94. Deviations-from-the-mean keeps every intermediate number one digit, the totals route makes you multiply 8 × 52 under pressure for no reason.

The eighth trade that moved your average

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