SOLUTION: Find the standard deviation. 44, 90, 73, 65, 76, 22, 50, 45, 37

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Question 165394: Find the standard deviation. 44, 90, 73, 65, 76, 22, 50, 45, 37
Answer by Edwin McCravy(20081)   (Show Source): You can put this solution on YOUR website!

List them in a column headed x
Draw a line and add the column

    x
   44 
   90 
   73 
   65
   76
   22 
   50 
   45
   37
-----
  502

Divide the 502 by 9, the number of numbers

    x
   44 
   90 
   73 
   65
   76
   22 
   50 
   45
   37
-----
9)502
 ----
   55.777···
                  _
That is the mean, x.  Subtract it from every value,
and place it in a column just to the right:
             _ 
    x      x-x
   44   -11.77···
   90    34.22···
   73    17.22···
   65     9.22···
   76    20.22···
   22   -33.77··· 
   50    -5.77··· 
   45   -10.77···
   37   -18.77···
-------------------
9)502
 ----
   55.777···

Square every term in that column, and
place those in a column to the right,
and add them:
             _         _ 
    x      x-x      (x-x)²
   44   -11.77···   138.716 
   90    34.22···  1171.160 
   73    17.22···   296.605
   65     9.22···    85.049
   76    20.22···   408.938
   22   -33.77···  1140.938 
   50    -5.77···    33.383
   45   -10.77···   116.160
   37   -18.77···   352.605
---------------------------
9)502              3743.554 
 ----
   55.777···

Divide that by 1 less than 9, or 8

             467.944
           ---------
          8)3743.554

Take the square root of 467.944

       

The standard deviation, s, is 21.632.

Edwin

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