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:

Answer 1

From the table:

$\sum f_i=30$

$\sum f_i{u}_i=-31$

And, class size of each interval $=0.04$

Let $x_i$ be the class mark for each interval

$\Rightarrow x_i=\frac{Upperclasslimit+Lowerclasslimit}{2}$

Let us take $0.14$ as the assumed mean $\left(a\right)$

Mean, $\overline{x}=a+\left(\frac{\sum f_i{u}_i}{\sum f_i}\right)\times h$

$=0.14+\left(\frac{-31}{30}\right)\times 0.04$

$=0.14-0.04133$

$=0.09867$

$\approx 0.099ppm$

Therefore, mean concentration of $S{O}_2$ in the air $=0.099ppm$