Median of Six Values

Date: 03/21/2001 at 19:29:06
From: Breanna
Subject: Median of even number of values

The problem is to find the median:

1)  8,18,26,4,4,5,  ____

    4,4,5,8,18,26

        5+8 = 13

    IS  13 divided by  2 OR 6   and so doing is the answer

                                6.5  /   6   /  or  2.1  ?

Thanks from fifth-grader Breanna

Date: 03/22/2001 at 13:14:04
From: Doctor Twe
Subject: Re: Median of even number of values

Hi Breanna - thanks for writing to Dr. Math.

When there are is even number of values in the data, the median is the 
average of the middle two values. Since we are averaging TWO numbers 
(in your example, the 5 and the 8), we divide by 2. Thus the answer 
for your example is:

     Median = 13 / 2 = 6.5

Another way to think about this and verify that our answer makes sense 
is to recall what the median is supposed to tell us. Half the numbers 
in the data set are supposed to be less than or equal to the median, 
and half the numbers in the data set are supposed to be greater than 
or equal to the median.

With a median of 6.5, half the numbers (4, 4 and 5) are less than 6.5, 
while the other half (8, 18 and 26) are greater than 6.5.

If we thought that 2.17 was the median, no numbers would be less than 
the median and all of the numbers would be greater than the median. 
That would make no sense at all. The "average" isn't supposed to be 
smaller than ALL of the values in the data.

I hope this helps. If you have any more questions, write back.

- Doctor TWE, The Math Forum
  http://mathforum.org/dr.math/