Sample Variance

Date: 08/08/97 at 21:12:31
From: craig murray
Subject: Sample variance

4,5,2,6,4,3,4

Could you please help me understand the sample variance using the data 
above?

n = 7
X = 3.52

I am having a hard time understanding the problem. Thank you for any 
help.

Craig 

Date: 08/09/97 at 07:29:35
From: Doctor Anthony
Subject: Re: Sample variance

The most convenient formula for calculating variance, (s^2), is

           SUM(x^2)
    s^2 =  --------  -  MEAN^2
              n

Lay out the working in tabular form:


    x     f      f.x      f.x^2
  -------------------------------
    2     1       2         4
    3     1       3         9
    4     3      12        48 
    5     1       5        25    
    6     1       6        36
  -------------------------------
          7      28       122

       MEAN =  28/7  =  4

  Variance  =  122/7  -  4^2

       s^2  =  1.42857   and standard deviation  = s = 1.19523

Note that this is SAMPLE variance and s.d.  If you wish to estimate 
population variance from the sample, then you multiply sample variance 
by n/(n-1), in this case by 7/6.

Population variance =  (7/6)(1.42857)

                    =   1.66667
  
-Doctor Anthony,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/