Question

Find the mean of the following data using step-deviation method:

Class	500 – 520	520 – 540	540 – 560	560 – 580	580 – 600	600 – 620
Frequency	14	9	5	4	3	5

Answer 1

Class	Frequency `(f_i)`	Midvalues `(x_i)`	`u_i = ((x_i− A))/ ℎ =( (x_i− 550))/ 20`	`(f_i × u_i)`
500 – 520	14	510	-2	-28
520 – 540	9	530	-1	-9
540 – 560	5	550 = A	0	0
560 – 580	4	570	1	4
580 – 600	3	590	2	6
600 – 620	5	610	3	15
	`Ʃ f_i = 40`			`Ʃ (f_i × u_i) = -12`

Now, A = 550, h = 20, Ʃ` f_i = 40 and Ʃ (f_i × u_i) = -12`

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

      = `550+{20xx ((-12))/40}`

      = 550 – 6

      = 544

∴  x  = 544