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/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994-2013 The Math Forum