Measures of Dispersion

• The Range: high-low
• The standard deviation: S = sqrt((Σ(x-mean)²/(n-1)
• Steps to find standard deviation:
  • Calculate mean
  • Build the table

    x

    x-mean

    (x-mean)2

  • Add up the third column.
  • Divide this by n-1
  • Take the square root.
• Examples:

  Number 2
     High = 20
     Low = 16
     Range = 20 - 16 = 4
    
  Number 4
     High = 17
     Low = 11
     Range = 6
  
  Number 8
     m = 91
     x    x-m     (x-m)2
     84   -7        49
     88   -3         9
     90   -1         1
     95    4        16
     98    7        49
  
     σ(x-m)2 = 124
     S2 = 124/4 = 31
     S = 5.57
      

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