Question

Consider the following distribution of SO2 concentration in the air (in ppm = parts per million) in 30 localities. Find the mean SO2 concentration using assumed mean method. Also find the values of A, B and C.

Class interval	Frequency (fi)	Class mark (xi)	di = xi - a
0.00 - 0.04	4	0.02	-0.08
0.04 - 0.08	9	0.06	A
0.08 - 0.12	9	0.10	B
0.12 - 0.16	2	0.14	0.04
0.16 - 0.20	4	0.18	C
0.20 - 0.24	2	0.22	0.12
Total	`sumf_i=30`

Options

• -0.04, 0, 0.04, 0.5

• -0.04, 0, 0.04, 0.6

• -0.04, 0, 0.04, 0.2

• -0.04, 0, 0.04, 0.098

Answer 1

-0.04, 0, 0.04, 0.098

Explanation:-

The 4^th column in the table shown in question is a table of values of ‘d’.

d_i = x_i – a

Here

d_i = value of ‘d’ for i^th class mark row.

x_i = i^th class mark

a = assumed mean value

Applying given formula for 1^st class interval (0-0.04),

-0.08 = 0.02 - a

a = 0.1

Thus P = 0.1

Applying given formula for 2^nd class interval (0.04 - 0.08)

A = 0.06 - 0.1

A = -0.04

Similarly for 3^rdand 5^th classes d values are-

B = 0

C = 0.04

Mean = 0.098