Median and Middle

Date: 5/15/96 at 20:53:47
From: Anonymous
Subject: Statistical Problem

I would like to know how to find the median of two of the same numbers 
(2 and 2). I looked in a mathematics book (Integrated Mathematics, 
Course 1 by Dressler and Kessnan) but could not find the answer. The 
book stated that the median of a set of numbers with an even number of 
terms was the average of the two surrounding numbers. I would like a 
specific answer from you and I would appreciate it if you could also 
send some type of proof, since my teacher requested it. 

Thank you!

Date: 5/16/96 at 17:27:24
From: Doctor Jodi
Subject: Re: Statistical Problem

It seems to me that this question isn't terribly meaningful.  
Generally, we might want to get the statistics on a group of numbers 
in order to analyze a large group of dissimilar numbers.

The median is the "middle" number.  So if our set is arranged in order 
like this:

5 40 380 700 976

the median is the middle number, here 380.

If our set has an even number of numbers, there really isn't a middle.

3 8 20 38

Here the median is found by taking the middle two numbers, 8 and 20, 
and finding their average (14).  

If we wanted to do the same thing with your set:

2 2

We would take the middle two numbers (since the set is even) and 
average them.  (The average of these two numbers, since they are the 
same, will be 2.)

I'm not sure what sort of proof you're looking for; as I've said, this 
does not seem to be the most meaningful sort of median, but I do 
believe that it follows the definition of median.  I hope this helps.

-Doctor Jodi,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/