Krishna
0

Step 1: Know about the step - deviation method

            The step-deviation method  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 = 70


                                          Deviation d = x_i - a


                                                         x_1= 50 , a = 70


                                                          d = 50 - 70 = - 20


Step 3: Calculate the deviation for every observation (See the table)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 us still apply the step deviation method with a = 70 and h = 55 - 45 = 10.


                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


                                                     = 70 + \frac{-2}{35}*10


                                         Mean = 70 - 0.5714


                                        Hence, Mean = 69.42