GEEK ALERT: When Mean Isn't Median AND Median Isn't Mode

GEEK SPEAK WARNING!  However, discussed in a way all can understand.


Quick definitions -- Median = Half Above/Half Below; Mode = Most Commonly Observed Data Point;  Mean = Average.  Take your standard bell curve.

On this curve,the vertical line in the center represents the mean, median, and mode.  But in the "real" world the results we observe don't always fit this curve.  Let's focus this discussion on the question of Median and Mode.  I'll save the Mean, no pun intended, discussion for a later time.


In the 2008 Presidential Election, our model generated the following chart:

What the reader should note is that the model projected average outcome of Obama 347 McCain 191.  However, the Mode, or most common outcome was 364-174.  The Mode proved to be dead on.  Actual result 365-173.  Difference -- Nebraska's split electoral vote. 


In analyzing the 2006 Senate races, an earlier version of our Model suggested Republicans had a 63% percent probability of holding the Senate.  As we all know, Republicans failed to defend their three state firewall of MO, TN, and VA and lost the Senate.  


HOWEVER, if one looks at our model's (earlier version) most common outcome among the possible combinations the actual outcome corresponded with the most likely individual combination of outcomes.


Here's an excerpt from an analysis from Friday, November 3, 2006.

This scenario has received most of the press recently as a probable scenario that will play out on election night.  The general notion is that whoever wins two out of three in Virginia, Tennessee and Missouri will control the Senate. 

Under this scenario, there is a 62.6% probability that Republicans will control the Senate with at least a 50-50 split plus the Vice President.

There are eight possible combinations of outcomes ranging from losing all three to winning all three.

Republicans would control the Senate under three of the four most likely outcomes.

Most Likely       R (TN) D (MO, VA)     Democrat 51-49       20.8%

2^nd Most Likely  R (TN, MO) D (VA)    Republican 50-50     19.4%

3^rd Most Likely   R (TN, VA) D (MO)   Republican 50-50     19.1%

4^th Most Likely   ALL R                     Republican 51-49      17.8%

Over the last few days posts here will examine the "most common" outcomes presented by the models.  History suggests this measure may be more significant than the other statistical measures the models.


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