Krishna
0

Step 1: Recall the formula of the mean of the grouped data

            NOTE: The mean (or average) of observations is the sum of the values of

              all the observations divided by the total number of observations.


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

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


                    Mean = \frac{f_1x_1 + f_2x_2 + ........f_nx_n}{f_1 + f_2 +..........+ f_n}


                                  or


                        Mean = \frac{\Sigma f_ix_i}{\Sigma f_i} 


              GIVEN:  The pocket allowance mean = 18

                            Find the missing frequency = ?


Step 2: Re-organize given data in the table and find the sum of all observations.

            

            


          Sum of the values of all the observations \Sigma f_ix_i=752\ +\ 20f


                Total number of observations \Sigma f_i=44\ +\ f


                          So, the mean = \frac{752\ +\ 20f}{44\ +\ f}

                          

Step 3: Find the missing frequency

                   Given Mean = 18

                  So,     18 = \frac{752 + 20f}{44 + f}


               18 * (44 + f) = 752 + 20f


                   18f - 20f = 752 - 792


                             -2f = - 40


                                  f = \frac{40}{2}


                                   f = 20

                Hence, the missing frequency f = 20