Mathematics

Find the mean age in years from the frequency distribution given below :
Age in years No. of persons
25 - 29 4
30 - 34 14
35 - 39 22
40 - 44 16
45 - 49 6
50 - 54 5
55 - 59 3

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The above data is discontinuous converting in continuous data we get,

Adjustment factor = (Lower limt of one class - Upper limit of previous class) / 2

$= \dfrac{30 - 29}{2} \\[1em] = \dfrac{1}{2} \\[1em] = 0.5$

Classes before adjustment	Classes after adjustment	Class mark (u_i)	No. of persons (f_i)	f_iu_i
25 - 29	24.5 - 29.5	27	4	108
30 - 34	29.5 - 34.5	32	14	448
35 - 39	34.5 - 39.5	37	22	814
40 - 44	39.5 - 44.5	42	16	672
45 - 49	44.5 - 49.5	47	6	282
50 - 54	49.5 - 54.5	52	5	260
55 - 59	54.5 - 59.5	57	3	171
Total			70	2755

Mean = $\dfrac{Σf$ = 39.36 years

Hence, the mean age = 39.36 years.

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