To find out the concentration of SO 2 in the air (in parts per million, i.e., ppm), the data was collected for 30 localities in a certain city and is presented below: Concentration of SO 2 (In ppm) Frequency 0.00-0.04 4 0.04-0.08 9 0.08-0.12 9 0.12-0.16 2 0.16-0.20 4 0.20-0.24 2 Find the mean concentration of SO 2 in the air.

Question

Philoid · Accepted Answer

We may calculate class marks (x_i) for each interval by using the relation

x_i =

Class size = 0.04

Now taking 0.14 as assumed mean (A), we can calculate as follows:

Concentration So₂ (ppm)	Frequency (f_i)	x_i	d_i = x_i – 0.14	u_i	f_iu_i
0.00-0.04	4	0.02	-0.12	-3	-12
0.04-0.08	9	0.06	-0.08	-2	-18
0.08-0.12	9	0.10	-0.04	-1	-9
0.12-0.16	2	0.14	0	0	0
0.16-0.20	4	0.18	0.04	1	4
0.20-0.24	2	0.22	0.08	2	4
	N = 30				∑f_iu_i = -31

Mean (x̅) = A + * h

= 0.14 + * (0.04)

= 0.14 – 0.04133

= 0.099ppm

SO, mean concentration of SO₂ in the air is 0.099ppm

Concentration of SO₂ (In ppm)	Frequency
0.00-0.04	4
0.04-0.08	9
0.08-0.12	9
0.12-0.16	2
0.16-0.20	4
0.20-0.24	2