Question

There is a grouped data distribution for which mean is to be found by step deviation method.

Class interval	Number of Frequency (fi)	Class mark (xi)	di = xi - a	`u_i=d_i/h`
0 - 100	40	50	-200	D
100 - 200	39	150	B	E
200 - 300	34	250	0	0
300 - 400	30	350	100	1
400 - 500	45	450	C	F
Total	`A=sumf_i=....`

Find the value of A, B, C, D, E and F respectively.

Options

• 186, -100, -200, -2, -1 and 2

• 188, -100, 200, -2, -1 and 2

• 188, 100, -200, 2, -1 and -2

• 186, 100, -200, -2, -1 and 2

Answer 1

188, -100, 200, -2, -1 and 2

Explanation:-

∑f_i = sum of frequencies of each class = 40 + 39 + 34 + 30 + 45 = 188

d_i = x_i - a

where x_i = i^th class mark

a = assumed mean

Using above formula for 1^st class (0 - 100) we get

-200 = 50 - a

a = 250

Using above formula for 2^nd class (100-200) we get

B = 150 - 250

B = -100

Similarly, C = 200.

`u_i = d_i/ h`

Here h = class interval = 100. h is constant.

For 1^st class (0 - 100),

`u_i = d_i/ h= -200/100 =-2`

Thus, D = -2

Similarly E = -1, F = 2

A, B, C, D, E and F are 188, -100, 200, -2, -1 and 2 respectively.