Question

To find out the concentration of $S{O}_2$ 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. Find the mean concentration of $S{O}_2$ in the air.

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

Answer 1

Let's find the mean concentration of $S{O}_2$ in the air.

Let us find determine Class Mark ($x_i$) for the following class intervals by using the formula

$Classmark=\frac{\left(Upperclasslimit+Lowerclasslimit\right)}{2}$

Concentration of SO2 (in ppm)	Frequency (fi)	Mid-point (xi)	fixi
0.00-0.04	4	0.02	0.08
0.04-0.08	9	0.06	0.54
0.08-0.12	9	0.10	0.90
0.12-0.16	2	0.14	0.28
0.16-0.20	4	0.18	0.72
0.20-0.24	2	0.20	0.40
Total	Sum fi = 30	Sum (fixi) = 2.96

The formula to find out the mean is

$Mean=\overline{x}=\frac{{\displaystyle \sum _{}^{}}{f}_i{x}_i}{\sum _{}^{}{f}_i}$

$$\begin{gathered} =\frac{2.96}{30} \\ =0.999ppm \end{gathered}$$

Therefore, the mean concentration of $S{O}_2$ in the air is $0.0999ppm$.