 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that from the following data find the mode by grouping method when it is not possible to find the model value by inspection then we prepare a grouping and analysis table. With this key idea let us proceed with the solution. By inspection it is difficult to say which is the model value though the highest frequency is 25 the concentration appears to be greater around 24. Hence we should prepare a grouping and analysis table. For grouping table first of all we write the frequencies 3, 6, 2 and so on in column 1. Now group by 2s that is 3 and 6, 2 and 20, 24 and 12 and so on and write their total 3 plus 6 is 9 2 plus 20 is 22, 24 plus 12 is 36 and so on in column 2 leave the last frequency 3, leave the first frequency that is 3 and group the remaining series by 2s. Write their total in column 3 that is 6 plus 2 is 8, 20 plus 24 is 44 and so on. Now group by 3 that is 3, 6 and 2, 20, 24 and 12, 5, 25 and 7 and write their total in column 4 that is 3 plus 6 plus 2 is 11 and so on. Leave the last frequencies 1 and 3. Leave the first frequency and group the remaining by 3s that is 6, 2 and 20, 24, 12 and 5 and 25, 7 and 1 and write their total in column 5 that is 28, 41 and 33. Leave the last frequency 3, leave the first 2 frequencies 3 and 6 and group the remaining by 3 that is 2, 20 and 24, 12, 5 and 25, 7, 1 and 3 and write their total in column 6 that is 46, 42 and 11. Now, circuit the highest frequency of each column that is 25 in column 1, 36 in column 2, 44 in column 3, 56 in column 4, 41 in column 5 and 46 in column 6. After grouping table, analysis table is prepared. Now, to prepare the analysis table, we put the column numbers on the left hand side and the model values of each column on the right hand side. Now enter into columns the highest frequencies marked in the grouping table that is for column 1, the highest frequency is 25 whose value is 8. So, mark the value of x equal to 8 in column 1. For second column, highest frequency is 36 whose values are 5 and 6. So, mark the value of x equal to 5 and 6 in column 2. For column 3, the highest frequency is 44 whose x values are 4 and 5. So, mark the values for x equal to 4 and 5 in column 3. For column 4, the highest frequency is 56 whose x values are 4, 5 and 6. So, mark the values for x equal to 4, 5 and 6 in column 4. For column 5, the highest frequency is 41 whose corresponding x values are 5, 6 and 7. So, mark the values for x equal to 5, 6 and 7 in column 5. For column 6, the highest frequency is 46 whose corresponding x values are 3, 4 and 5. So, mark the values for x equal to 3, 4 and 5 in column 6. Now take the total of each column that is 1, 3, 5, 3, 1, 1. Now the value which is repeated maximum number of times is 5 and the x value against which the total is the highest is the mode. From the analysis table, 5 occurs. The maximum number of times thus mode is given by 5 which is the required answer. This completes our session. Hope you enjoyed this session.