Question

Find the arithmetic mean of the following frequency distribution using step-deviation method:

Age (in years)	18 – 24	24 – 30	30 – 36	36 – 42	42 – 48	48 – 54
Number of workers	6	8	12	8	4	2

Answer 1

Class	Frequency `(f_i)`	Mid values `(x_i)`	`u_i =( (x_i− A))/ ℎ = ((x_i− 33))/ 6`	`(f_i× u_i)`
18 – 24	6	21	-2	-12
24 – 30	8	27	-1	-8
30 – 36	12	33 = A	0	0
36 – 42	8	39	1	8
42 – 48	4	45	2	8
48 – 54	2	51	3	6
Total	`Ʃ f_i = 40`			`Ʃ (f_i × u_i) = 2`

Now, A = 33, h = 6, `Ʃ f_i = 40 and Ʃ (f_i × u_i) = 2`

∴ Mean, x = A + `{ h xx (Ʃ (f_i × u_i))/(Ʃ f_i)}`

                 =`33+ { 6xx2/40}`

                 = 33 + 0.3
                 = 33.3
∴ x = 33.3 years