 Hello and welcome to the session. I am Shashi and I am going to help you with the following question. A survey was conducted by a group of students as a part of their environment awareness program in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house. This is the given data. Which method did you use for finding the mean and why? First of all, let us understand that mean is equal to summation f i x i upon summation f i. Now in this formula, x bar is the mean, f i is the frequency and x i is midpoint of the class interval. Or we can say it is class knock of the given class interval. This is the direct method of finding the mean and we will use this as our key 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 the given data represents number of plants and number of houses. Now first of all, let us find out class mark that is x i for every class interval. Let us recall that class mark is equal to upper class limit plus lower class limit upon 2. So 2 plus 0 upon 2 is equal to 1. Similarly 4 plus 2 upon 2 is equal to 3. Here also midpoint of this interval is equal to 5. Similarly 6 plus 8 upon 2 is equal to 7. Here 10 plus 8 upon 2 is equal to 9. Here midpoint of this interval is 11. Similarly midpoint of this interval is 13. Now we know number of houses represent the frequency so we will denote it by f i. Let us now find out the product f i x i. Here 1 multiplied by 1 is equal to 1. 2 multiplied by 3 is equal to 6. 1 multiplied by 5 is equal to 5. 5 multiplied by 7 is equal to 35. Similarly 6 multiplied by 9 is equal to 54. 2 multiplied by 11 is equal to 22. And 3 multiplied by 13 is equal to 39. Now we will find out summation f i by adding all these frequencies. And we know this is the data for 20 houses. So sum of these frequencies is equal to 20. Let us now find out summation f i x i. Summation f i x i is equal to sum of all these products. And sum of all these products is equal to 162. Now from key idea we know mean is equal to summation f i x i upon summation f i. Now substituting corresponding values of summation f i x i and summation f i in this formula. We get mean is equal to 162 upon 20. Now we will cancel common factor 2 from numerator and denominator both. And we get mean is equal to 81 upon 10 which is further equal to 8.1. Here we have used direct method for finding the mean. Here clearly we can see given values of f i and x i are small. So it becomes easy to multiply these corresponding values. So we can say direct method of finding the mean is used when values of f i and x i are small. So the required answer is mean number of plants per house is equal to 8.1 plants we have used. Direct method for finding the mean because the numerical values of x i and f i are small. This is our required answer. This completes the session. Hope you understood the solution. Take care and have a nice day.