Given below is the concentration of SO₂ in air (in ppm = parts per million) in 30 localities:
$\begin{matrix} S O_{2} concentration (in ppm) & Number of localities 0.00 - 0.04 & 4 0.04 - 0.08 & 9 0.08 - 0.12 & 9 0.12 - 0.16 & 2 0.16 - 0.20 & 4 0.20 - 0.24 & 2 \end{matrix}$
Find the mean of $S O_{2}$ concentration using assumed - mean method.
0.099

Open in App

Solution

The correct option is A 0.099
Let assumed mean, i.e., $a = 0.10$ . Now let us form the table and tabulate the mean of $S O_{2}$ concentration:

$\begin{matrix} C l a s s i n t e r v a l & F r e q u e n c y (f_{i}) & C l a s s m a r k (x_{i}) & d_{i} = x_{i} - a & f_{i} d_{i} 0.00 - 0.04 & 4 & 0.02 & - 0.08 & - 0.32 0.04 - 0.08 & 9 & 0.06 & - 0.04 & - 0.36 0.08 - 0.12 & 9 & 0.10 & 0.00 & 0.00 0.12 - 0.16 & 2 & 0.14 & 0.04 & 0.08 0.16 - 0.20 & 4 & 0.18 & 0.08 & 0.32 0.20 - 0.24 & 2 & 0.22 & 0.12 & 0.24 T o t a l & \sum f_{i} = 30 & \sum f_{i} d_{i} = - 0.04 \end{matrix}$

$M e a n = (x) = a + \frac{\sum f_{i} d_{i}}{\sum f_{i}} = 0.10 + \frac{- 0.04}{30} = 0.099$

So, the mean of $S O_{2}$ concentration = 0.099

Suggest Corrections

Similar questions

Question 7
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:

$\begin{matrix} Concentration of S O_{2} (in pmm) & Frequency 0.00 - 0.04 & 4 0.04 - 0.08 & 9 0.08 - 0.12 & 9 0.12 - 0.16 & 2 0.16 - 0.20 & 4 0.20 - 0.24 & 2 \end{matrix}$

Find the mean concentration of $S O_{2}$ in the air.

Consider the following distribution of SO2 concentration in the air(in ppm = parts per million) in 30 localities. Find the mean SO2 concentration using assumed mean method. Also find the values of A, B and C

$\begin{matrix} C l a s s I n t e r v a l & F r e q u e n c y (f_{i}) & C l a s s m a r k (x_{i}) & d_{i} = x_{i} - a 0.00 - 0.04 & 4 & 0.02 & - 0.08 0.04 - 0.08 & 9 & 0.06 & A . . . . . . . . . 0.08 - 0.12 & 9 & 0.10 & B . . . . . . . . 0.12 - 0.16 & 2 & 0.14 & 0.04 0.16 - 0.20 & 4 & 0.18 & C . . . . . . . . 0.20 - 0.24 & 2 & 0.22 & 0.12 T o t a l & \sum f_{i} = 30 \end{matrix}$

\begin{matrix} {Concentration of SO}_{2} (in ppm) & Number of days (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 Total & 30 \end{matrix}

The above frequency distribution table represents the concentration of Sulphur dioxide in the air in parts per million of a certain city for 30 days. Using this table,
find the probability of the concentration of Sulphur dioxide in the interval 0.12−0.16 on any of these days.

Consider the following distribution of SO₂ 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. Find the mean.

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

Join BYJU'S Learning Program

Given below is the concentration of SO2 in air (in ppm = parts per million) in 30 localities: SO2 concentration (in ppm)Number of localities0.00−0.0440.04−0.0890.08−0.1290.12−0.1620.16−0.2040.20−0.242 Find the mean of SO2 concentration using assumed - mean method.0.099