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Question

# 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)Frequency0.00−0.0440.04−0.0890.08−0.1290.12−0.1620.16−0.2040.20−0.242 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=xi−0.14xi=xi−0.14hfiui0.00−0.0440.02−0.12−3−120.04−0.0890.06−0.08−2−180.08−0.1290.10−0.04−1−90.12−0.1620.140000.16−0.2040.180.04140.20−0.2420.220.0824Total30 −31 From the table, we may observe that: ∑fi=30∑fiui=−31Mean ¯x=a+(∑fiui∑fi)×h=0.14+(−3130)(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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