Question

Find the mean of each of the following frequency distributions

Class interval	50 - 70	70 - 90	90 - 110	110 - 130	130 - 150	150 - 170
Frequency	18	12	13	27	8	22

Answer 1

Let the a assumed mean be 100

Class interval	Mid-value (x1)	d1 = x1 - 100	`"u"_1 = (x_1 - 100)/20`	f1	f1u1
50 - 70	60	-40	-2	18	-36
70 - 90	80	-20	-1	12	-12
90 - 110	100	0	0	13	0
110 - 130	120	20	1	27	27
130 - 150	140	40	2	8	16
150 - 170	160	60	3	22	66
				N = 100	`sumf_1"u"_1=61`

A = 100, h = 20

Mean `A+hxx(sumf_1"u"_1)/N`

`=100+20xx61/100`

`=100+1220/100`

= 100 + 12.20

= 112.20