Krishna
0

Step 1: Recall the step-deviation method

           The step-deviation method are just simplified form of

           the direct method.


           Let x_1, x_2, x_3............, x_n be observations with respective

          frequencies f_1, f_2,............f_n


                Mean = a + \frac{\Sigma f_iu_i}{\Sigma f_i}*h


                  Where, u_i = \frac{d_i}{h}


                     d_i = x_i - a

                    a - Assumed mean

                    h - is the class size.


Step 2: Choose one among the observations as the assumed mean, and Find the deviation of ‘a’ from each of the observations


          NOTE: It is taken somewhere in the middle of all the values of observations

                            Assumed mean a = 225


                                    Deviation d = x_i - a

                                                     x_1= 125, a = 225

                                                  d = 125 - 225 = - 100

                      Calculate the deviation for every observation (See the table)


Step 3: Divide the deviation by the class size (h) to calculate u_i

                               u_i = \frac{d_i}{h}


            Class size (h): Generally size of the class is taken as h but it need not

            be size of the class always.

                  

            Let apply the step deviation method with a = 225 and h = 150 - 100 = 50.

                              u_1=\frac{-100}{50}=-2


              Then, we obtain the data as given in the table.

                    


Step 4: Calculate the mean using the step deviation formula


                  Step deviation mean = a + \frac{\Sigma f_iu_i}{\Sigma f_i}*h


                                                   = 225 + \frac{-7}{25}*50


                                       Mean = 225 - 14


                                  Hence, Mean = 211