Find the mean of the following data, using assumed-mean method:
$\begin{array}{ccccccc}\text{Class}& 0-20& 20-40& 40-60& 60-80& 80-100& 100-120\\ \text{Frequency}& 20& 35& 52& 44& 38& 31\end{array}$

Solution:

Class	Frequency (fi)	Mid values (xi)	Deviation (di) di = (xi - 50)	(fidi)
0-20	20	10	-40	-800
20-40	35	30	-20	-700
40-60	52	50 = A	0	0
60-80	44	70	20	880
80-100	38	90	40	1520
100-120	31	110	60	1860
Total	∑fi=220

∑(fi×di)=2760

Mean, $\overline{x}$=A+∑(fi×di)/∑fi

Let A = 50 be the assumed mean.

Then we have:

= 50 + 2760/220

= 50 + 12.55

Therefore, $\overline{x}$ = 62.55