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.
0.098

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Solution

The correct option is A 0.098
Let assumed mean, i.e., $a = 0.10$

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

$M e a n = (x) = a + \frac{\sum f_{i} d_{i}}{\sum f_{i}} = 0.10 + \frac{- 0.04}{30} = 0.098$
$∴$ the mean of $S O_{2}$ concentration is 0.098 ppm.

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

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

\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}

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Q. 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.

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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.0.098