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Suppose ten distinct, positive integers have a median of 10. ("Distinct integers" means that no two integers are the same.)

What is the smallest the average of those ten integers could be?

Explain your answer in complete sentences.

JohnyGotchaApples Dec 10, 2018

#1**+2 **

Don't know that this is the correct answer, JGA....but here's my best attempt :

If we have 10 ditinct positive integers....the median is the average of the 5th and 6th data values [ assuming the we have ordered the values in increasing order from left to right ]

It's obvious that the first four integers will be 1, 2, 3 , 4

To have the smallest overall average, we need to have the 5th and 6th values as close to 10 as possible such that their average is 10.....these are 9 and 11

And the remaining integers are 12, 13, 14 and 15

So....the data set is

1,2, 3, 4, 9, 11, 12, 13, 14, 15

The median = 10

The average = 8.4

CPhill Dec 10, 2018