Measurement type Dispersion

The purpose of measures of dispersion is to find out how to spread out the data values are on the number line.

 The range of a set of  data  is the difference between the largest and smallest values

                   Range = Maximum value - Minimum value

     

Range = 39-9
       =30

VARIANCE  is the expectation of the squared deviation of a random variable from its mean, It measures how far a set of numbers are spread out from their average value.

Sample variance

population variance

            1.Calculating the Sample variance for the values: 4, 7, 8,9, 11
                
                We have to find mean for the following values : 4 + 7 + 8 + 9 + 11 / 5 = 39 / 5 
                                                                                          
                                                                              Mean = 7.8
                           

                     S^2  = (4-7.8)^2 + (7-7.8)^2 + ( 8-7.8)^2 + (9-7.8)^2 + (11-7.8)^2 / 5-1
                             = 6.7 
                               
                    Therefore, the sample variance is 6.7                                                                        

    STANDARD DEVIATION  is a measure that is used to quantify the amount of variation or      dispersion of a set of data values
    
    we can find standard deviation by adding square root to variance 
    we will get zeros if you won't square them 

     Population Standard Deviation:
           
      PS =  {4 , 7 , 8 ,9 ,11}
         
           mean  = 7.8 

    

 = sqrt(5.36) = 2.32

     

  
    SAMPLE STANDARD DEVIATION:
   

     SS={4,7,8,9,11}

      Mean= 7.8

  = sqrt(6.7)  =2.59