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[Solved] Average arithmetic mean

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The average (arithmetic mean) of eight numbers is 7. If two numbers are discarded, the average of
the remaining numbers is . What is the average of the two discarded numbers?

A)            B)            C)            D)           E)  17

1 Answer
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Draw some average pies! The first pie is for all 8 numbers, which average 7. This pie is going to be split into two groups, so you need two more pies, one for the remaining 6 numbers, and one for the discarded two. The average for the remaining 6 numbers is 6.5, which means the total is 39. Subtract that from the previous total of 56 from the first pie, 7 x 8, to get the remaining total 17. 17 is the total for the two discarded number pie, so the average is  \small 8\tfrac{1}{2}.

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