CLASS-9
MEAN & MEDIAN - UNGROUPED FREQUENCY DISTRIBUTION - STEP DEVIATION METHOD

UN-GROUPED FREQUENCY DISTRIBUTION -

iii) STEP DEVIATION METHOD-

When the values of yᵢ and fᵢ are large and the values of yᵢ are equally spaced, we use the step deviation method for the purpose of finding the mean, as described below –

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

Step.2) Then we have to calculate h = (y₂ - y₁)

                                                       (xᵢ - A)

Step.3) In this stage we have to calculate uᵢ = ----------- for each i

                                                          h

Step.4) Now we have to calculate fᵢuᵢ for each i and hence find Ʃ fᵢuᵢ

Step.5) Now we should calculate the mean using the formula

                                      Ʃ fᵢuᵢ

                   y = A + h X ----------

                                      Ʃ fᵢ

Example) The measurement (in mm) of the diameters of the heads of 10 screws are given below –

Calculate the mean diameter of the heads of the screws, using the step deviation method.

Ans.) Clearly, h = (37 – 34) = 3

Let, the assumed mean be A = 40

Then, we may prepare the table given below.

                                           Ʃ fᵢuᵢ

Mean,  y  =  A + { h X --------- }

                              Ʃ fᵢ

                               24

            =  40 + {3 X ---------}

                               100

            =  40 + 0.72

            =   40.72       

Hence, mean diameter = 40.72 mm   (Ans.)