Question

Find the mean of the following frequency distribution, using the assumed-mean method:

Class	100 – 120	120 – 140	140 – 160	160 – 180	180 – 200
Frequency	10	20	30	15	5

Answer 1

Class	Frequency (fi)	Mid values (xi)	Deviation (di) di = (xi – 150)	(fi × di)
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
	Ʃ fi = 80			Ʃ(fi × di) = -300

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

Mean, x = `A + (Ʃ (f_i × d_i))/(Ʃ f_i)`

= 150 + `(-300)/80`

= `(1200-30)/8`

= `1170/8` 

∴ x = 146.25