Question

Consider the following distribution of $S{O}_2$ concentration in the air(in ppm = parts per million) in 30 localities. We wish to find the mean SO₂ concentration using step assumed mean method.Fill the following table. Determine the assumed mean(a) and proceed.

$$\begin{array}{ccccc}ClassInterval& Frequency\left(f_i\right)& Classmark\left(x_i\right)& d_i=x_i-a& \\ 0-100& 40& 50& -200& D......\\ 0.00-0.04& 4& 0.02& -0.08& \\ 0.04-0.08& 9& 0.06& A.........& \\ 0.08-0.12& 9& 0.10& B........& \\ 0.12-0.16& 2& 0.14& 0.04& \\ 0.16-0.20& 4& 0.18& C........& \\ 0.20-0.24& 2& 0.22& 0.12& \\ Total& \sum f_i=30& & & \end{array}$$

The value of A, B and C respectively are:

• A. 0.04, 0 and 0.08
• B. 0.3, 0 and 0.3
• C. 0.2, 0 and 0.3
• D. 0.2, 0 and 0.3

Answer 1

The correct option is A

0.04, 0 and 0.08

The $4^{th}$ column in table shown in question is a table of values of ‘d’.

$d_i=x_i-a$

Here

$d_j$ = value of ‘d’ for $i^{th}$ class mark-row.

$x_i$ = $i^{th}$ class mark

a = assumed mean value

Applying given formula for $1^{st}$ class interval(0-0.04),

-0.08 = 0.02 – a

a = 0.1

Thus P = 0.1

Applying given formula for 2nd class interval(0.04-0.08)

A = 0.06 – 0.1

A = -0.04

Similarly for $3^{rd}$ and $5^{th}$ classes d values are-

B = 0

C = 0.04