Question 617183
find the variance, and standard deviation for the following set of scores:
<pre>
Add them.

   X                                         
   4                                      
   2                                      
   2                                      
   3                                      
   5
   6
 ---
  22

Out beside that column square every number, that is, multiply
it by itself, then add that column and you have:

     X      X²                                         
     4      16                                   
     2       4                                  
     2       4                                  
     3       9                                  
     5      25
     6      36 
   ---     --- 
 &#8721;x=22  &#8721;x²=94

The variance is s².  The short-cut formula is:
   
     n(&#8721;X²) &#8722; (&#8721;X)²
s² = --------------
       n(n &#8722; 1)

We substitute  &#8721;x=22,  &#8721;x²=94, and n=6 (the number of numbers)

     6(94) &#8722; (22)²
s² = -------------- 
       6(6 &#8722; 1)

      564 &#8722; 484
s² = -------------- 
         6(5)

          80
s² = -------------- 
          30

s² = {{{8/3}}} = 2.66666666667

That's the variance.

To get the standard deviation, take the square root:

s = {{{sqrt(s^2)}}} = {{{sqrt(8/3)}}} = 1.632993162

Round off all answers to the nearest hundredth.

s² = 2.67

 s = 1.63

Edwin</pre>