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Question -

To find out the concentration of SO_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:



Answer -


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 meanconcentration of SO2 in the air.


Solution:

To find out the mean, first find the midpointof the given frequencies as follows:

Concentration of SO2 (in ppm)

Frequency (fi)

Mid-point (xi)

fixi

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 fi = 30

Sum (fixi) = 2.96

The formula to find out the mean is

Mean = x̄ = ∑fixi /∑fi

= 2.96/30

= 0.099 ppm

Therefore, the mean concentration of SO2 inair is 0.099 ppm.

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