 Hi and welcome to the session. Today we will learn about mode and median. So first of all let us start with mode of grouped data. Mode is that value among observations which occurs most often. So to find out the mode of the given data we will first find the modal class. In modal class is the class with the maximum frequency. Then we can find mode using the formula L plus F1 minus F0 upon 2F1 minus F0 minus F2 into H where L is the lower limit of the modal class is the class size. Assuming all class sizes to be equal is the frequency modal class. 0 is the frequency of the class preceding the modal class. F2 is the frequency of the class succeeding the modal class. Let us take one example to understand this. So here we are given class intervals and frequency corresponding to each class interval and we need to find mode. So first of all we will find the modal class and as we can see that in these frequencies 20 is the maximum frequency. So the class corresponding to the frequency 20 that is 200 to 250 will be the modal class. So we have modal class as 200 to 250. So here L will be 200 that is the lower limit of the modal class which will be equal to 250 minus 200 that is 50. Here this will be F1 F0 and 10 will be F2. Now let us find mode and mode is given by the formula L plus F1 minus F0 upon 2F1 minus F0 minus F2 into H. Now substituting these values we will get 200 plus 20 minus 5 upon 2 into 20 minus 5 minus 10 into 50. So this will be equal to 230. So here mode is equal to 230. Now let us move on to median of group data. Median is the measure of central tendency which gives the value of the middle most observation in the data. To find out median we will first of all find the median class. In class is the class whose cumulative frequency is greater than or is to the value N upon 2 where N is number of observations. Then we can find out median using the formula L plus N upon 2 minus CF upon F into H where N is lower limit of median class. N is number of observations. F is cumulative frequency preceding the median class. F is the frequency of median class and H is the class size assuming all class sizes to be equal. Now let us find out the median for the same data. Here we have class intervals, frequency. Now let us make the column for cumulative frequency. Here cumulative frequency will be 6, 6 plus 3, 9, 9 plus 5, 14, 14 plus 20, 34, 34 plus 10, 44. So here number of observations that is N is equal to 44. Now let us find out the median class first. For that we have N equal to 44. So this implies N upon 2 will be equal to 22. Now the cumulative frequency which is greater than and nearest to 22 is 34. That means the class corresponding to 34 that is 200 to 250 will be the median class. So here we have median class as 200 to 250. So N that is the lower limit of the median class will be equal to 200 upon 2 is 22. Now CF that is the cumulative frequency of the class preceding to the median class is 14 and F that is the frequency of median class will be 20. Finally H will be equal to the class size that is 250 minus 200 which is equal to 50. Now let us find out median which is given by the formula N plus N upon 2 minus CF upon F into H. Now substituting the values we will get 200 plus 22 minus 14 upon 20 into 50 and this will be equal to 220. So here median is equal to 220. Now there is a spherical relationship between mean, median and mode. That relationship is 3 times median is equal to mode plus 2 times median. With this we finish this session hope you must have understood all the concepts. Goodbye take care and have a nice day.