 In this video, we are going to learn about finding mean by assumed mean method and we have some data of age of people in society. The class interval shows the ages here and the frequency shows the number of people in that age range. So the frequency for 10 to 20 years is 3, 20 to 30 years is 6. That means there are 3 people aged between 10 to 20. 6 people aged between 20 to 30 and so on. Now our objective here is to find the mean age in the society given to us. We know different methods exist to find the mean. We can simply find the class mark for each. Class mark is the midpoint of the class intervals. So let's just quickly write it. One of the methods is that we can multiply the class mark with the frequency. So here the class mark is 15. In order to find the class mark, what we do is we add the lower and upper limits and divide it by 2. So we get 15. Similarly for the second one, 20 plus 30, 50 divided by 2 is 25 and so on. So we can complete writing the class marks. So if I write mean as x bar, one of the methods is to sum up fi xi divided by summation fi. That means multiplying each frequency and the respective class mark and then summing that up and then dividing it by the total number of frequency. Sometimes the procedure becomes complicated when the multiplication becomes complicated and in such instances what we do is we first assume some mean and once we assume that mean we find a deviation for each class mark from that mean. So the first step is to assume some mean. Now this assumed mean is somewhere in the middle when we arrange the class marks from in ascending order like this. So x1, x2, x3 and so on and we choose some middle value whatever to be the class mark. So here the class marks are 15, 25, 35, 45 and 55. We can choose our assumed mean to be 35 here. So let's just write that. So here we are assuming that our assumed mean is 35. Now we are interested in finding the deviation or DI for each class interval. So for class mark 15 this 35 is nothing but A. So the deviation will be that class mark minus the assumed mean. So in this case it will be 15 minus 35 which is minus 20. Similarly if we keep on doing the same process 25 minus 35 this is going to give me minus 10. Then 35 minus 35 is simply 0. For 45 minus 35 we get 10 and for 55 minus 35 we get 20. Now we are interested in finding F i DI. That means the multiplication of the frequency and the respective deviations. So for the first row we get minus 20 times 3 which is minus 60. And we can complete rest of the rows as follows. We get minus 10 times 6 which is minus 60 again. Then 0 times 8 which is 0. Then 10 times 4 which is 40 and then 20 times 5 which is 100. So in the next step what we do is then we sum up the values in the last column F i DI. So here the summation is minus 60 minus 60. So let me just quickly write it here. Summation F i DI is equal to minus 60 minus 60 plus 0 plus 40 plus 100. And that gives me 20. Let me also sum up all the frequencies. The summation of all the frequencies is 9 plus 8 17 plus 4 21 and 21 plus 5 as 26. Now I am ready to find the mean from assumed mean method. So the mean is found as A which is the assumed mean plus summation F i DI divided by summation F i. So basically we are adding some deviation term in the assumed mean from the data that we have. And we have already found summation F i DI which is 20 and summation F i which is 26. So we can find the mean as A which is 35 here plus summation F i DI that is 20 divided by 26. And this gives me 35.77. Let me just box it real nice like this and this is how we can find the mean by assumed mean method.