Krishna
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Step 1: Know about the deviation or assumed mean method

          The assumed mean method (or 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_id_i}{\Sigma f_i}


                      Where, d_i = x_i - a

                            a - Assumed mean


Step 2: Choose one among the observations as the assumed mean, and denote it by 'a'

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

                        Assumed mean a = 57


Step 3: Find the deviation of ‘a’ from each of the observations ( x_i 's)

                Deviation d = x_i - a


                                 x_1 = 51, a = 57


                                 d = 51 - 57 = - 6

                Calculate the deviation for every observation (See the table)


Step 4; Find the product of d_i(deviations) with the corresponding frequencies f_i, and take the sum of all the f_id_i's.


               Calculations are shown in table given below

                    


Step 5:  Find the mean of the deviations

                     Mean of the deviations = a + \frac{\Sigma f_id_i}{\Sigma f_i}


                                                          = 57 + \frac{75}{400}


                                                Mean = 57 + 0.1875


                                                  Mean = 57.1875