Question

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 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.

Answer 1

Answer:-

Concentration of $S{O}_2$ (in ppm)	$x_i$	Frequency $\left(f_i\right)$	$f_i{x}_i$
0.00-0.04	0.02	4	0.08
0.04-0.08	0.06	9	0.54
0.08-0.12	0.10	9	0.90
0.12-0.16	0.14	2	0.28
0.16-0.20	0.18	4	0.72
0.20-0.24	0.22	2	0.44
		$\Sigma f_i=30$	$\Sigma f_i{x}_i=2.96$

$\text{mean concentration of}S{O}_2\text{in the air}=\frac{\Sigma f_i{x}_i}{\Sigma f_i}=\frac{2.96}{30}=0.0986\approx 0.099$