 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that calculate the mode from the following data. The marks are represented by x and are given in the range of 0 to 5, 5 to 10, 10 to 15, 15 20, 20 to 25, 25 to 30, 30 to 35 with the corresponding number of students represented by f given by 3, 5, 10, 20, 12, 6, 3. Mode is given by the formula m0 is equal to l1 plus fn minus f1 upon twice of fn minus f1 minus f2 into i where l1 is the lower limit of the modal class fn is the frequency of the modal class 1 is the frequency of the class preceding the modal class is the frequency of the class succeeding the modal class is the width of the modal class the idea let us proceed with the solution we are given the following distribution since the given series is regular we can locate the modal group by inspection and we find that the class interval 15 to 20 is the modal class since it has the maximum frequency that is 20 by inspection we can say that the modal class is 15 to 20 now from the key idea we know that mode m0 is given by l1 plus fn minus f1 upon twice of fn minus of f1 minus of f2 into i where l1 is the lower limit of the modal class fn is the frequency of the modal class f1 is the frequency of the class preceding the modal class f2 is the frequency of the class succeeding the modal class and i is the width of the modal class so we have mode m0 is equal to l1 plus f minus f1 upon twice of fn minus f1 minus f2 into i is equal to l1 that is the lower limit of the modal class which is equal to 15 plus fm that is the frequency of the modal class which is 20 minus f1 that is the frequency of the class preceding the modal class that is given by 10 upon twice of fn that is 2 into 20 minus f1 that is 10 minus f2 that is the frequency of the class succeeding the modal class which is given by 12 into i that is the width of the modal class which is given by 20 minus 15 that is 5 therefore we have m0 is equal to 15 plus 20 minus 10 that is 10 upon 2 into 20 that is 30 minus 10 minus 12 that is minus of 22 into 5 which is equal to 15 plus 10 upon 30 minus 22 that is 18 into 5 that is 15 plus 5 into 5 that is 25 upon 9 which is equal to 15 plus 25 upon 9 can be written as 2.77 so we have 15 plus 2.77 that is 17.77 so m0 is equal to 17.77 therefore the mode for the given series is given by 17.77 which is the required answer this completes our session hope you enjoyed this session