Question

To find the concentration of $S{O}_2$ in the air (in parts, per
million), the data was collected for 30 localities, in a certain city
and is presented below:

Concentration of $S{O}_2$ (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 concentrations of $S{O}_2$ in the air.

• A. $0.099$ ppm
• B. $0.09$ ppm
• C. $0.99$ ppm
• D. $0.0909$ ppm

Answer 1

The correct option is A $0.099$ ppm

Consider the following table, to calculate mean:

$ci$	$f_i$	$x_i$	$f_i{x}_i$
$0.00-0.04$	$4$	$0.02$	$0.08$
$0.04-0.08$	$9$	$0.06$	$0.54$
$0.08-0.12$	$9$	$0.10$	$0.90$
$0.12-0.16$	$2$	$0.14$	$0.28$
$0.16-020$	$4$	$0.18$	$0.72$
$0.20-0.24$	$2$	$0.22$	$0.44$

$N=\Sigma f_i=30$

$\Sigma f_i{x}_i=2.96$

Mean $\overline{x}=\frac{\Sigma f_i{x}_i}{N}$

$\therefore \overline{x}=\frac{2.96}{30}=0.0986667\approx 0.099$

mean concentration of $S{O}_2$ in air is $0.099ppm$

Hence, option $A$ is correct.