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Question 7
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 pmm)Frequency0.000.0440.040.0890.080.1290.120.1620.160.2040.200.242

Find the mean concentration of SO2 in the air.

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Solution

We may find the class marks for each interval by using the relation:

xi =Upper class limit + lower class limit2

Class size of this data = 0.04

Now, taking 0.14 as assumed mean a, we may calculate di,ui,fi,ui as following:

Concentration of SO2(in pmm)FrequencyClass mark xidi=xi0.14xi=xi0.14hfiui0.000.0440.020.123120.040.0890.060.082180.080.1290.100.04190.120.1620.140000.160.2040.180.04140.200.2420.220.0824Total30 31

From the table, we may observe that:

fi=30fiui=31Mean ¯x=a+(fiuifi)×h=0.14+(3130)(0.04)=0.140.04133=0.099 ppm

So, mean concentration of SO2 in the air is 0.099 ppm.


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