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