How to find Mean of Grouped Data:

(iii) Method 3: The Step Deviation Method:

Let $u_i= {x_i-a}/{h}$

where $a$ is the assumed mean and $h$ is the class size. 

Let  $ū$ = ${Σf_i u_i }/{Σf_i}$

We have  $u_i$ = ${x_i-a}/{h}$

Therefore  $ū$ = ${{Σf_i(x_i-a)}/h}/{Σf_i}$ 
= $1/h$ ${[{Σf_ix_i}/{Σf_i}$ -$a{Σf_i}/{Σf_i}$${ ]}$
			 $ū$  =$1/h$ $[{x̄-a}]$
			 $hū$  =$[{x̄-a}]$
			 $x̄$  =$a$+$h ū$
			 
			 $x̄$  =$a$+$h({Σf_i u_i }/{Σf_i})$