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Note that for a set of consecutive integers, the median is the the average of the first and the last integer 

M
Dec 10th, 2015

Thank you for the opportunity to help you with your question!

Let  {x, x+1, x+2, x+3, x+4, x+5 }  be a set of even number of consecutive integers. 

The median  M  =  the average of two middle numbers  =  [(x + 2) + ( x +3 )] / 2  =  (2x + 5)/2

Now the average of the first and last integer  =  [ x + ( x + 5)]/2  =  ( 2x + 5)/2

median = the average of the first and last integer. 


Let { x, x +1, x +2, x +3, x +4,  x +5, x+6}  be a set of odd number of consecutive integers. 

The median is the middle integer  =  x +3

Now the average of the first and last integer  =  ( x + x +6)/2  = (2x +6)/2  = x+3.

So we proved for even and odd number of consecutive integers. Hence it is true for any set of integers. 

Please let me know if you need any clarification. I'm always happy to answer your questions.
Dec 10th, 2015

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