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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:

 Concentraion 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.

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We may calculate class marks (xi) for each interval by using the relation

xi \(=\frac{Upper\,class\,limit+lower\,class\,limit}{2}\)

Class size = 0.04 

Now taking 0.14 as assumed mean (A), we can calculate as follows:

 Concentration So2 (ppm)  Frequencey (fi)  xi  di = xi - 0.14 ui fiui
 0.00 - 0.04 4 0.02 -0.12 -3 -12
 0.04 - 0.08 9 0.06 -0.08 -2 -18
 0.08 - 0.12 9 0.10 -0.04 -1 -9
0.12 - 0.16 2 0.14 0 0 0
0.16 - 0.20 4 0.18 0.04 1 4
0.20 - 0.24 2 0.22 0.08. 2 4
 N = 30 \(\sum\)fiui = -31

Mean (x̅) = A + \(\frac{\sum f_iu_i}{N}\times h\)

\(=0.14+\frac{-31}{30}\times(0.04)\)

\(=0.14-0.04133\)

\(=0.099\)ppm

SO, 

mean concentration of SO2 in the air is 0.099 ppm

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