Question

 The following is the cumulative frequency distribution ( of less than type ) of 1000 persons each of age 20 years and above . Determine the mean age .

Age below (in years):	30	40	50	60	70	80
Number of persons :	100	220	350	750	950	1000

Answer 1

Let the assumed mean A = 45 and h = 10.

Marks	Mid-Value(xi)	Frequency (fi)	`u_1 = (x_1 - 45)/10`	`f_iu_i`
20–30	25	100	-2	-200
30–40	35	120	-1	-120
40–50	45	130	0	-0
50–60	55	400	1	400
60–70	65	200	2	400
70–80	75	50	3	150
		N - 1000		`sum"f"_"i""u"_"i" = 630`

We know that mean,  `barX = "A"+"h" (1/"N" sum"f"_"i""u"_"i")`

Now, we have

N = `sum`f_i = 1000, h = 10, A = 45, `sum`f_i u_i = - 370\]

Mean = `bar"x"` = a + h `((sum"f"_"i""u"_"i")/(sum"f"_"i"))` 

= 45 + 10`(630/1000)`

= 45 + 6.3

= 51.3 years