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What is the largest possible median for the five number set \(\{x, 2x, 3, 2, 5\}\)  if  can be any integer?

 Sep 22, 2020
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When a list of numbers is sorted in sequence, the median is the number in the center of the list.  In other words, there are the same amount of numbers less than the median as the amount of numbers more than the median.  

 

Example:  In the list  1  2  3  15  100  200  300  the median number is 15.   

 

Note particularly that the median is not synonymous with the average. 

 

So in the list in the above problem, sorted from lowest to highest, is  2  3  5  x  2x    

 

The largest possible median is 5.  The value of x can be anything larger than 5. 

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 Sep 22, 2020

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