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Six numbers from a list of nine integers are 7, 8,12 ,15 ,19 , and 5. What is the largest possible value of the median of all nine numbers in this list?

 Nov 18, 2020
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Six numbers from a list of nine integers are 7, 8,12 ,15 ,19 , and 5. What is the largest possible value of the median of all nine numbers in this list?   

 

Here's the way I see it.  The nine integers are 5, 7, 8, 12, 15, 19, n7, n8, and n9   

 

The median is the number which there are the same number of values less than it as there are values more than it. 

 

In this example, with nine values in ascending order, the median would be the fifth value, to wit, 15

 

It doesn't matter what specific values n7, n8, and n9 have; just so long as they're larger than 15.  

 

If n7, n8, and/or n9 are smaller than 15, then that moves the median down, and the problem asks for the largest.  

.

 Nov 18, 2020

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