 Hi and welcome to the session. Today we will learn about mean of group data. We can find out mean using three methods. First direct method, second assumed mean method and third step deviation method. We will learn all these three methods one by one with the help of examples. Suppose we want to find out mean for the given data. For this we will find out mean for all the three methods. So first of all let us make the columns for class interval and frequency. So here we have class intervals 0 to 10, 10 to 20, 20 to 30, 30 to 40 and 40 to 50 and the frequency corresponding to these class intervals is 12, 16, 6, 7, 9. We denote frequency by f i. So first of all we will find out the class mark for these class intervals. Now let us see what is class mark. Class mark is equal to upper class limit plus lower class limit upon denote class mark by x i. So here for class interval 0 to 10 class mark will be 0 plus 10 upon 2 that is 5 for 10 to 20 it will be 15, then 25, then 35 and lastly 45. Now first of all we will find out mean using direct method. The formula used in direct method is mean denoted as x bar is equal to sigma fi x i upon sigma fi. Here fi is the frequency x i is the class mark and sigma fi x i means sum of multiplication of fi and x i. So here we have the column for fi x i. Now we will make the column for fi x i. So here 12 into 5 is 60, 16 into 50 is 240, 6 into 25 is 150, 7 into 35 is 245 and 9 into 45 is 405. So sigma fi x i is equal to 1100 and here sigma fi is equal to 50. So let us find out mean that is x bar which is equal to sigma fi x i upon sigma fi. Now substituting the values of sigma fi x i and sigma fi we will get 1100 upon 50 which is equal to 22. So our mean is 22. This method is known as direct method. Now let us move on to assumed mean method. This method the formula to find out mean that is x bar is a plus sigma fi di upon sigma fi where a is assumed mean i is x i minus a that is assumed mean. For this let's see the same example again. Now first of all we want to find out the value of a that is assumed mean. We take assumed mean that is a to be that number which lies in between or in the center of x i that is these numbers. So here we can take 25 as the assumed mean. So let us write assumed mean that is a is equal to 25. Now let's make the column of di which is equal to x i minus a. So 5 minus 25 is minus 20 15 minus 25 is minus 10 25 minus 25 is 0 35 minus 25 is 10 and 45 minus 25 is 20. Now according to the formula we need to find out sigma fi di. So for that let's make the column of fi di and for this we will multiply each fi with its corresponding di. So 12 into minus 20 is minus 240 then we have minus 160 0 70 and 180 and sigma fi di is equal to minus 150. So let us quickly find out the mean that is x bar which is given by the formula a plus sigma fi di over sigma fi. So substituting the values we get a that is 25 plus sigma fi di that is minus 150 upon sigma fi that is 50. Solving this we get 22. So mean is equal to 22. So this was the assumed mean method. Now we will learn stick deviation method. Here the formula to find out mean is a plus h into sigma fi ui upon sigma fi where a is assumed mean h is class size ui is x i minus a upon h. Now we will apply this method to the same example in this we already know how to find out assumed mean. So we have assumed mean equal to a equal to 25. Now here class size is 10 minus 0 that is 10. So here h is equal to 10. Now if we see our formula then we need to find ui that is x i minus a upon h. So here we will find out ui which is equal to x i minus a upon h. This will be equal to minus 2 minus 1 0 1 2. Now we need to find out sigma fi ui. So we will make the column of fi ui. For this we will multiply each fi with its corresponding ui. Thus we get minus 24 minus 16 0 7 18 and sigma fi ui is equal to minus 15. So let's find out mean that is x bar and it is given by the formula a plus h into sigma fi ui upon sigma fi. So this will be equal to a that is 25 plus h that is 10 into sigma fi ui that is minus 15 upon sigma fi that is 50. On solving this we will get 22. So by this method also our mean is equal to 22. This is our step deviation method. So in this session we have learnt direct method to find out mean, assume mean method and step deviation method to find out mean. With this we finish this session hope you must have understood all the methods. Goodbye take care and have a nice day.