Question

Given below is the concentration of SO₂ in air(in ppm = parts per million) in 30 localities:
$\begin{array}{cc}S{O}_2\text{concentration (in ppm)}& \text{Number of localities}\\ 0.00-0.04& 4\\ 0.04-0.08& 9\\ 0.08-0.12& 9\\ 0.12-0.16& 2\\ 0.16-0.20& 4\\ 0.20-0.24& 2\end{array}$
Find the mean of $S{O}_2$ concentration using assumed - mean method.

• A. 0.1
• B. 0.123
• C. 0.144
• D. 0.16

Answer 1

The correct option is B

0.123

Let assumed mean, i.e., $a=0.10$

$\begin{array}{ccccc}\text{Class interval}& \text{Frequency}\left(f_i\right)& \text{Class mark}\left(x_i\right)& d_i=x_i-a& f_i{d}_i\\ 0.00-0.04& 4& 0.02& -0.08& -0.32\\ 0.04-0.08& 9& 0.06& 0.04& 0.36\\ 0.08-0.12& 9& 0.10& 0.00& 0.00\\ 0.12-0.16& 2& 0.14& 0.04& 0.08\\ 0.16-0.20& 4& 0.18& 0.08& 0.32\\ 0.20-0.24& 2& 0.22& 0.12& 0.24\\ Total& \sum f_i=30& & & \sum f_i{d}_i=0.68\end{array}$

$Mean=\left(x\right)=a+\frac{\sum f_i{d}_i}{\sum f_i}=0.10+\frac{0.68}{30}=0.123$

So, the mean of $S{O}_2$ concentration = 0.123