What is a Median?

Date: 03/03/98 at 22:58:44
From: SEAN
Subject: What is median?

What is a median?

Date: 03/05/98 at 11:12:55
From: Doctor Johnny
Subject: Re: What is median?

Sean,

I hope that I can help you better understand the definition of median 
and what it really deals with.

By definition, a median is a statistical term identifying a piece of 
data (number) that divides numerically ordered data into two equal 
halves. In easier terms, the median is the middle piece of data when 
those data are placed in numerical order.

Let's look at two examples. One example has an odd number of pieces of 
data, and another has an even number of pieces.

45
46
46
47------> Median because there are 3 pieces above and 3 pieces below
50
57
60


45
46
46
47
50
--------> 53 is the median ***Explanation below***
56
60
61
62
62

The reason 53 is the median is because the median falls halfway 
between the numbers 50 and 56.

As a rule, the piece of data that represents the median can be found 
by using the following formula:

  N+1  (N is the number of pieces of data)
 ----- 
   2   because the median divides the set of data into 2 equal pieces.  

Proof of the examples: 

 7 pieces of data
 
   7+1
   --- = 4th piece of data
    2

                       
 10 pieces of data
 
   10+1
   ---- = 5.5th piece of data 
    2

(This piece is located halfway between the 5th and 6th piece of data, 
because 5.5 is halfway between 5 and 6.)

I hope that this will help you to better understand median and how it 
is found.

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