CLASS-9
MEAN & MEDIAN- UNGROUPED FREQUENCY DISTRIBUTION- ASSUMED MEAN METHOD

UN-GROUPED FREQUENCY DISTRIBUTION -

ii) ASSUMED MEAN METHOD-

When the product fᵢyᵢ involves large numbers, we use the assumed mean method for finding the mean and proceed step wise as under.

Step.1) We have to choose a suitable value of yᵢ in the middle as the assumed mean and call it A.

Step.2) Now, we should calculate the deviation dᵢ = (yᵢ - A) for each yᵢ

Step.3) Now, we have to calculate the product fᵢdᵢ for each i

Step.4) Now, we have to find the value of Ʃ fᵢdᵢ and Ʃ fᵢ

Step.5) Now, we have to calculate the mean using the formula –

                        Ʃ fᵢdᵢ

      Mean = A + -----------

                         Ʃ fᵢ

Example) Using the assumed mean method, find the mean weekly wages from the data given below –

Ans.) Let the assumed mean A = 140

Now, we can arrange the given data as under.

                                             Ʃ fᵢdᵢ

       Mean, y = A  + -------------

                               Ʃ fᵢ

                               180

                 = 140 + ----------

                                71

                 =  140 + 2.54 

                 =   142.54

Hence mean weekly wages = $ 142.54    (Ans.)