Question 188631
10,23,28,4,1,6,12

<pre>

 1. List the numbers under X.
 2. Add them, getting 84.
 3. Count them, there are 7
 4. Divide <u>8</u>4 by 7, getting 12.  
    That's x, the mean.
 5. Subtract 12 from each number,_ 
    place it under the heading X-X
 6. Sq<u>u</u>are each number under the heading
    X-X and put it <u>u</u>nder
    the heading (X-X)<sup>2</sup>         _  
 7. Add those numbers under (X-X)<sup>2</sup> 
 8. Divide by 1 less that the number of numbers, that is,
    there are 7 numbers so divide by 1 less
    or 6, getting 100.3333333, that's called the "variance", s<sup>2</sup> 
 9. Take the square root of 100.3333333, getting s = 10.0166528
10. The range is the largest number minus the smallest number, 28-1 or 27.
        _      _    _ 
   X -  X =  X-X (X-X)<sup>2</sup>  
------------------------
  10 - 12 =  -2     4
  23 - 12 =  11   121
  28 - 12 =  16   256
   4 - 12 =  -8    64
   1 - 12 = -11   121
   6 - 12 =  -6    36
  12 - 12 =   0     0
 ---             ----
7)84           6) 602
 ---   _         ----
  12 = X          100.3333333 = s<sup>2</sup>
                  ___________
                 <font face = "symbol">Ö</font>100.3333333 = 10.0166528 = s

The largest value is 28 and the smallest value is 1, so the
range is 28-1 or 27.

Your other problem is done the same way.

The mean is $370
The standard deviation is $267.3325021
The range is $850-$100 = $750

Edwin</pre>