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Rating System Editorials - Trimmed Mean

Author: 
Rick Burton
Trimmed Average or Trimmed Mean:


(From my old Statistics book) : Trimmed Mean is a comprimise between (True) Average and Median.


While True Average uses all data points (votes on our case) to determine a representative value for the set of data, Median excludes all values but the 1 to 2 "middle" values and uses this value(s) to determine the representative value.  Trimmed Average of a data set excludes the highest and lowest X% of the data points and takes the average of the remainder.


For example:  Take mod with the following votes:


10, 10, 9, 9, 9, 9, 8, 8, 8, 1


a 10% Trimmed Average would "trim" the 1st and 10th numbers (since they are the highest and lowest 10%) and average the remaining 8 votes.


The 10% Trimmed Average of the mod would be: 8.75


For comparison on the same data set:


Average: 8.1


Median : 9.0




Not only does Trimmed Average remove outlier data (votes that are so far from what most people vote, that it overly influences the True Average) like Median, but it also does not group a lot of mods with similar voting patterns with the same score (having 19 mods scored at 10.0) like True Average.


Trimmed Average is the best of both worlds.  But why is Trimmed Average similar to both Median and True Average?  It is because Median and True Average are the two extremes of Trimmed Average.


True Average is 0% Trimmed Average.
Median is approximately 50% Trimmed Average.



The only question is what people feel the best X% that should be used with Trimmed Average for the present voting system.  Maximus has stated that if Trimmed Average wins the poll, another would be held to determine the most appropriate X%.

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