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To find out the concentration of SO2 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:
Concentration of SO2 ( in ppm) 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
Find the mean concentration of SO2 in the air.


Answer :

Calculate mean by direct method:

Concentration of SO2 (in ppm) Frequency \( ( f_i ) \) Mid-point \( (x_i) \) \( f_i x_i \)
0.00 - 0.04 4 0.02 0.08
0.04 - 0.08 9 0.06 0.54
0.08 - 0.12 9 0.10 0.90
0.12 - 0.16 2 0.14 0.28
0.16 - 0.20 4 0.18 0.72
0.20 - 0.24 2 0.20 0.40
Total \( \sum f_i \ = \ 30 \) \( \sum f_i x_i \ = \ 2.96 \)

The formula to find out the mean is

\( \overline{x} \ = \ \frac{ \sum \ f_i x_i}{ \sum f_i} \)

\( = \ \frac{2.96}{30} \)

\( = \ 0.099 \) ppm

\(\therefore \) The mean concentration of SO2 in air is 0.099 ppm.

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