Data Tables

Calculating the mean () and standard deviation (SD, ) of a set of data

  The mean is the average value of a group of data.  
  The formula is:

     

  For example, if we consider the following data set:



  

    
10
  
  

    
8
  
  

    
10
  
  

    
8
  
  

    
8
  
  

    
4
  



  the number of samples (n) is 6

  the mean is

      = (10 + 8 + 10 + 8 + 8 + 4) / 6 
       =  8

  We can judge how far the data samples are spread around the 
  mean value by calculating the variance and standard deviation  
  (SD, ) of the data set as follows:

     

     

  A standard deviation value close to 0 means the data samples are 
  grouped very close to the mean.

  For the sample data set above, the variance of the data set is

      

  or 4.8.  The standard deviation is

     

  or 2.19.  In this example, 5 out of 6 (83%) of the data samples are within
  one standard deviation from the mean.

  Note:  Usually at least 68% of all the samples will fall inside one standard 
    deviation (higher or lower) from the mean.  Approximately 95% of the data 
    will fall within two standard deviations from the mean.

  Samples of tables with number of samples (n), mean, standard deviation 
  information:

    
              Click on image for larger view

    
              Click on image for larger view

    
              Click on image for larger view