AMC 12A 2012 #8
Posted:
Fri Jun 15, 2012 9:35 pmby nsguy1350
An iterative average of the numbers 1, 2, 3, 4, and 5 is computed the following way. Arrange the five numbers in some order. Find the mean of the first two numbers, then find the mean of that with the third number, then the mean of that with the fourth number, and finally the mean of that with the fifth number. What is the difference between the largest and smallest possible values that can be obtained using this procedure?
Re: AMC 12A 2012 #8
Posted:
Sat Jun 16, 2012 12:20 pmby darksaber21
So, they are basically saying this is how to find the average:
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The minimum number can be obtained with the following order:
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The maximum number can be obtained with the following order:
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It makes sense why when you actually do it. Anyway, so now you just perform the action for both sequences and find the difference between the mean of both:
First for the minimum:
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Now for the maximum:
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Now for the difference:
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