Question

Find the mean of the following data, using assumed-mean method:
$\begin{array}{cccccc}\text{Marks}& 100-120& 120-140& 140-160& 160-180& 180-200\\ \text{Number of students}& 10& 20& 30& 15& 5\end{array}$

Answer 1

Class	Frequency (fi)	Mid values (xi)	Deviation (di) di = (xi - 150)	(fidi)
100 - 120	10	110	-40	-400
120 - 140	20	130	-20	-400
140 - 160	30	150 = A	0	0
160 - 180	15	170	20	300
180 - 200	5	190	40	200
Total	∑fi=80			∑(fi×di)=−300

Let A = 150 be the assumed mean. Then we have:

Mean, $\overline{x}$=A+[∑(fi×di)/∑fi]

= 150 + (-300/80)

= 150 - 3.75

Therefore, $\overline{x}$= 146.25