Question

To find out the concentration of SO₂ 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 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

Find the mean concentration of SO₂ in the air.

Answer 1

To find the class marks for each interval, the following relation is used:

`x_i  = ("Upper class limit + Lower class limit")/2`

Class size of this data = 0.04

Taking 0.14 as the assumed mean (a), d_i, u_i, f_iu_i are calculated as follows:

Concentration of SO2 (in ppm)	Frequency fi	Class mark xi	di = xi − 0.14	`u_i=(x_i-0.14)/0.04`	fiui
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
Total	30				−31

From the table, we obtain

`sumf_i = 30`

`sumf_iu_i = -31`

mean `barx=a+(sumf_iu_i)/(sumf_i)xxh`

`= 0.14 + ((-31)/30)(0.04)`

= 0.14 − 0.04133

= 0.09867

= 0.099 ppm

Therefore, mean concentration of SO₂ in the air is 0.099 ppm.