Question

calculate the arithmetic mean by step deviation method from the following data.
X : 10,20,30,40,50,60,70,80
f:4,10,18,20,24,14,6,4

Answer 1

Karan,

X	f	Deviation(d= X- A), A= 40	$(\mathrm{d}\text{'}=\frac{\mathrm{X}-\mathrm{A}}{\mathrm{C}})$ C = 10	fd'
10	4	10 - 40 = -30	-3	-12
20	10	20 - 40 = -20	-2	-20
30	18	30 - 40 = -10	-1	-18
40	20	40 - 40 = 0	0	0
50	24	50 - 40 = 10	1	24
60	14	60 - 40 = 20	2	28
70	6	70 - 40 = 30	3	18
80	4	80 - 40 = 40	4	16
	$\mathrm{\Sigma f}=100$			Σfd'=36

$$\begin{gathered} \overline{X}=A+\frac{\Sigma fd\text{'}}{\Sigma f}\times C \\ \overline{X}=40+\frac{36}{100}\times 10 \\ \overline{X}=43.6 \end{gathered}$$