Krishna
1

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 = 200


                    Deviation   d = x_i - a


                              x_1=\ 40, a = 200


                                  d = 40 - 200 = - 160


                    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.

            Here, the class size varies, and the x_i's are large.

            Let us still apply the step deviation method with a = 200 and h = 20.

            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


                                               = 200 + \frac{-106}{45}*20


                                  Mean = 200 - 47.11


                      Hence, Mean = 152.89