Mean Less Than Median

Date: 08/17/2003 at 08:43:21
From: Charmaine
Subject: Mean < Median

Can you draw any valid conclusions about a set of data in which the 
mean is less than the median?

Normally the mean is greater than or about the same as the median; 
however, if the mean is less than the median, what can we conclude 
from the set of data?

Date: 08/17/2003 at 09:51:19
From: Doctor Douglas
Subject: Re: Mean < Median

Hi Charmaine,

Thanks for writing to the Math Forum.

This can occur if the extreme values on the small end are farther
from the mean than the extreme values on the high side:

  {1,1,99,99,100,100,100}

Here the median is 99, but the mean is 71.4.  The two small values
skew the mean downward.  

I'm not sure that this answers your question.  Please write back
if you have any more questions about this.

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

Date: 08/18/2003 at 07:13:20
From: Charmaine
Subject: Thank you (Mean < Median)

Thank you Doc Douglas for the information that you have provided... it 
gives me a clearer picture now.

Thank you once again. :)