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