Measures of Dispersion

• This is another way to describe the data.
• These measures are a way to describe how spread out the data is.
• range = highest value - lowest value
• The standard deviation is a second measure
  • s² = Σ(x-x)²/(n-1)
  • (We normally express s but I can't do a square root in html)
  • This is much more difficult to compute, but it is a better measure.
• Consider the following data sets

                 DATA              x    range     s
    A:   1 3 7 8  9 12 15 17 18    10     17    5.98
    B:   8 9 9 9 10 10 11 11 13    10      5    1.5
    

• Range only considers the two extremes, while standard deviation considers all values.
• To find the standard deviation
  • Find x
  • List the data values in order in a table.
  • In the second column calculate x- x
  • In the third column calculate (x-x)²
  • Sum the (x-x)² column.
  • Divide this by the number of data items -1
  • Take the square root.
• Consider problem 26, page 793

  x = (60 + 100 + 85 + 35 + 250 + 150 + 300)/7
    =  980/7 = 140
  
          x     x-x  (x-x)2
         60     -80   6400
        100     -40   1600
         85     -55   3025
         35    -105  11025
        250     110  12100
        150      10    100
        300     160  25600
                    ------
  		   59850 
  
                    59850/6 = 9975 
  		  s = 99.87
        

Homework