Calculation of Standard Deviation

In statistics, standard deviation is used to measure deviation of data from its mean. The formula for calculating standard deviation of n items is

                        __________            

          s    =   Ö  variance

                     

where       

                          1        _n

  variance =       -----       S   (x_i-m)²

                           n       ⁱ⁼¹

and                          1         _n

         m = mean =  ------    S   x _i

                                n        ⁱ⁼¹

The algorithm for calculating the standard deviation is as follows:

  1.    Read n items.

  2.    Calculate sum and mean of the items.

  3.    Calculate variance.

  4.    Calculate standard deviation.

  Complete program with sample output is shown in Fig.7.8.

PROGRAM TO CALCULATE STANDARD DEVIATION

Program

   #include <math.h>                                          

   #define   MAXSIZE    100                                   

                                                              

   main( )                                                     

   {                                                          

        int i,n;                                              

        float value [MAXSIZE], deviation,                     

              sum,sumsqr,mean,variance,stddeviation;          

                                                              

        sum = sumsqr = n = 0 ;                                

                                                              

        printf("Input values: input -1 to end \n");           

        for (i=1; i< MAXSIZE ; i++)                           

        {                                                     

            scanf("%f", &value[i]);                           

            if (value[i] == -1)                               

               break;                                         

            sum += value[i];                                  

            n += 1;                                           

        }                                                      

        mean = sum/(float)n;                                  

                                                              

        for (i = 1 ; i<= n; i++)                              

        {                                                      

            deviation = value[i] - mean;                      

            sumsqr += deviation * deviation;                  

        }                                                     

        variance = sumsqr/(float)n ;                          

        stddeviation = sqrt(variance) ;                       

                                                              

        printf("\nNumber of items : %d\n",n);                 

        printf("Mean : %f\n", mean);                          

        printf("Standard deviation : %f\n", stddeviation);    

   }                                                          

                                                              

   Output                                                      

                                                              

   Input values: input -1 to end                              

   65  9  27  78  12  20  33  49  -1                          

                                                               

   Number of items : 8                                        

   Mean : 36.625000                                           

   Standard deviation : 23.510303