Question

Find the mean of the following distribution:

Class	10 - 25	25 - 40	40 - 55	55 - 70	70 - 85	85 - 100
Frequency	2	3	7	6	6	6

Answer 1

Class Interval	Frequency (fi)	c.f.	xi	`bb(U_i = (x_i - a)/h`	fiui
10 - 25	2	2	17.5	– 3	– 6
25 - 40	3	5	32.5	– 2	– 6
40 - 55	7	12	47.5	– 1	– 7
55 - 70	6	18	62.50 = a	0	0
70 - 85	6	24	77.5	1	6
85 - 100	6	30	92.5	2	12
	Σfi = 30				Σfiui = – 1

Let a = Assumed Mean = 62.5

Mean, `bar(x) = a + (sumf_iu_i)/(sumf_i) xx h`

= `62.5 xx (-1)/30 xx 15`

= `62.5 - 1/2`

= 62.5 – 0.5

= 62