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### Sample Variance

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

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

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/
```
Associated Topics:
High School Statistics

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