 Hello and welcome to the session. I am Deepika here. Let's discuss a question which says the following data gives the information on the observed lifetimes in hours of 225 electrical components. Lifetimes in hours 0 to 20, frequency is 10, 20 to 40, 35, 40 to 60, 52, 60 to 80, 51, 80 to 100, 38 and 100 to 120, 29. Determine the modal lifetimes of the components. Now in this question, first we will locate a class with the maximum frequency called the modal class. The mode is of value inside the modal class and is given by the formula mode is equal to L plus F1 minus F0 upon 2F1 minus F0 minus F2 into H, where is the lower limit of the modal class which is the size of the class interval. Frequency of the modal class is the frequency in the modal class. So is the frequency of the class in the modal class at the solution. They are given lifetimes in hours of the electrical components. Also its frequency is given to us. The number of electrical component whose lifetimes in hours is 0 to 20 is 10, group 20 to 40, the number of electrical components are 35 or that is the frequency is 35, 40 to 60, the frequency is 52 and in the group 60 to 80 the frequency is 61, in the group 80 to 100 frequency is 38 and in the group 100 to 120 the frequency is 29. Now here the maximum class frequency is 61 and the class corresponding to this frequency is 60 to 80. So the modal class is 60 to 80 which is equal to which is the lower limit of the modal class is 60, H is equal to 20 is equal to 61, 0 is equal to now F0 is the frequency of the class preceding the modal class. So this is 52 and F which is the frequency of the class succeeding the modal class and this is 38. Let us substitute these values in the formula mode is equal to plus F1 minus F0 upon 2F1 minus F0 minus F2 into H. So this is equal to 60 plus 61 minus 52 upon 2 into 61 minus 52 minus 38 into 20 and this is equal to 60 plus 9 upon 122 minus 52 minus 38 into 20 and this is equal to 60 plus 9 upon now 52 and 30 is 90, 122 minus 90 is 32 into 20. So on cancellation we have this is equal to 60 plus 45 upon 8 and this is equal to 60 plus now 45 upon 8 is 5.625 therefore mode is equal to 65.625 hours that is the modal lifetimes of the component is equal to 65.625 hours. Hence the answer for the above question is 65.625 hours. I hope the solution is clear to you. Bye and take care.