 Hi and welcome to the session. Let us discuss the following question. Question says to find out the concentration of sulphur dioxide in the air. The data was collected for 30 localities in a certain city and is presented below. This is the given data. Find the mean concentration of sulphur dioxide in the air. First of all, let us know that according to direct method, mean is equal to summation fi xi upon summation fi, where x bar is mean, fi is frequency, xi is class mark of interval or we can say it is midpoint of the interval. Now we will use this formula as basic idea to solve the given question. Let us now start with the solution. First of all, we will rewrite the data given in the question. Now we are given concentration of sulphur dioxide in parts per million and frequency. We denote frequency by fi. Now we will find out midpoint of every class interval or we can say we will find out class mark of every class interval. We denote class mark by xi. Now we know class mark is equal to upper class limit plus lower class limit upon 2. So 0.04 plus 0.00 upon 2 is equal to 0.02. Similarly, class mark of this class interval is equal to 0.06. Here it is equal to 0.10. For this interval, class mark is equal to 0.14. Now for this interval, midpoint of this interval is equal to 0.18 and midpoint of this interval is equal to 0.22. Now we will find the product fi xi. Now 4 multiplied by 0.02 is equal to 0.08. 9 multiplied by 0.06 is equal to 0.54. 9 multiplied by 0.10 is equal to 0.90. 2 multiplied by 0.14 is equal to 0.28. 4 multiplied by 0.18 is equal to 0.72. 2 multiplied by 0.22 is equal to 0.44. Now we will find out summation fi. Summation fi is equal to sum of all these frequencies. It is equal to 30 and summation fi xi is equal to sum of all these products. So it is equal to 2.96. From key idea, we know mean is equal to summation fi xi upon summation fi. Substituting corresponding values of summation fi xi and summation fi. In this formula, we get mean is equal to 2.96 upon 30. Now simplifying further, we get mean is equal to 0.0986. We can say mean is equal to 0.099. Rounding off this value up to 3 places of decimal, we get mean is equal to 0.099. So we get mean concentration of sulphur dioxide in the air is equal to 0.099 parts per million. This is our required answer. This completes the session. Hope you understood the session. Take care and have a nice day.