 Hello, and welcome to the session I am Deepika here. Let's discuss the question which says The following distribution gives the state-wise teacher-student ratio in high-scandry schools of India Find the mode and mean of this setup, interpret the two measures Now, if the number of students per teacher is 15 to 20, then the number of states or union territories having this ratio is 3 and if the number of students per teacher is 20 to 25, then the number of states or union territories having this ratio is 8 and for 25 to 30 it is 9, for 30 to 35 it is 10 For 35 to 40 it is 3, for 40 to 45 it is 0, for 45 to 50 it is 0 and for 50 to 55 it is 2 Now we know that the mean for the group data can be found by the direct method So by direct method new x1 is equal to sigma f i x i upon sigma f i where i is the frequency of the i-th class, x i is the class mark of the i-th class Now we can find the class mark by finding the average of its upper and lower limits Now to find mode we will first find the modal class that is we will locate a class with the maximum frequency and that will be called the modal class and the mode is a value inside the modal class and is given by the formula mode is equal to 1 minus f0 upon 2f1f0 minus f2 into is the load limit of the modal class h is the size of the class that is size of the class interval is the frequency of the modal class h is the frequency of the class exceeding the modal class So this is a key idea behind our question We will take the help of this key idea to solve the above question So let's start the solution Now we are given number of students per teacher and number of states or union territories Now if number of students per teacher is 15 to 20 then the number of states or union territories having this ratio is 3 and if the number of students per teacher is 20 to 25 then the number of states or union territories is 8 for 25 to 30 it is 9 for 30 to 35 it is 10 for 35 to 40 it is 3 for 40 to 45 it is 0 for 45 to 50 it is again 0 and for 50 to 55 it is 2 Now this is our f5 Now we will make a column for the class mark and we will find the class mark of each class that is x i Now the class mark of the class 15 to 20 is 15 plus 20 upon 2 that is 17.5 Now the class mark of the class 20 to 25 is 20 plus 25 upon 2 which is 22.5 Similarly for this class 30 upon 2 which is 27.5 and for this class it is 32.5 for this class 35 to 40 it is 37.5 for the class 40 to 45 it is 40 plus 45 upon 2 which is 42.5 and for the class 45 to 50 it is 47.5 and for the class 50 to 55 it is 52.5 We will multiply each x i with the corresponding frequency f5 Now 3 into 17.5 is 52.5 10 to 22.5 is 180 10 into 27.5 is 247.5 232.5 is 325 237.5 is 112.5 and 42.5 is 0 and 0 into 47.5 is again 0 and 2 into 52.5 is 105 Now we will find the sum of all the frequencies that is sigma f5 which is equal to 35 We will find sigma f5 x i is equal to 1022.5 So according to our key idea mean x bar is equal to x i upon sigma f5 and this is equal to 1022.5 upon 35 and this is equal to 29.2 of the data is equal to 29.2 Now we will find the mode of the above data Now to find mode we will first find the module class From this table the maximum frequency is having the maximum frequency is at module class is 30 to 35 Now equal to 30 to 35 So this implies which is a low limit of the module class is 30 which is the size of the class interval is 5 which is the frequency of the module class and it is 10 which is the frequency of the class preceding the module class So a frequency of the class succeeding the module class So f0 is 9 is 3 Now when substituting these values in the formula given by mode is equal to i plus f1 minus f0 upon 2f1 minus f0 minus f2 into h we have mode is equal to which is 30 plus which is 10 minus f0 which is 9 upon 2f1 that is 2 into 10 minus f0 which is 9 minus f2 which is 3 So this is equal to that is mode is equal to 30 plus 1 over 20 minus So mode is equal to 30 plus 5 upon 8 Now 5 upon 8 is equal to 0.625 So mode is equal to 30 plus 0.625 and this is equal to 30.6 Therefore of the given data is equal to 30.6 Now the name of the given data is 29.2 and the mode of the given data is 30.9 So in this case have a student teacher ratio of 30.6 on an average this ratio is 29.2 His answer for that question is mode 29.2 or union territory having teacher ratio 30.6 and on an average this ratio is 29.2 I hope the solution is clear to you Bye and take care