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Standard Deviation

Date: 05/17/99 at 15:53:03
From: Rob
Subject: Statistics, Standard Deviation

What is standard deviation?

Date: 05/17/99 at 18:03:21
From: Doctor Pat
Subject: Re: Statistics, Standard Deviation


The general idea of a standard deviation is that it is a typical 
amount to be different. Think of it this way: suppose the average 
height of 16-year-old males is 70 inches - but almost no one is 
EXACTLY 70 inches tall. If someone is 71 inches high you will probably 
still say he is pretty normal in height. Maybe even 72 inches, but at 
73 or 74 inches you would start to say that that person is NOT 
typical; he is on the tall side. 

This is sort of what the standard deviation does: it gives us a number 
to put on sets that says this is (more or less) an unusual measure for 
this population.  

To find it follow these easy steps:

  1) Find the average of the set

  2) Create a new set (the deviations) by subtracting the average from 
     each of the original numbers.

  3) Square each number in the set of deviations to make a set of 
     squared deviations

  4) Average the set of squared deviations

  5) Take the square root so that the answer has the same units as the 
     original measures  (ft or inches or whatever) 

This is called the root mean square deviation  because it is the ROOT 
of the MEAN of the SQUARE of the DEVIATIONS.

Hope that helps.

- Doctor Pat, The Math Forum   
Associated Topics:
High School Statistics

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