 Hi and welcome to the session. Today we will learn about Graphical Representation of Cumulative Frequency Curve. First of all let us learn to draw cumulative frequency curve as a dive of less than time. We will understand this with the help of an example. So here we are given scores obtained by the students of a class and the frequency corresponding to each class interval. Now to draw the cumulative frequency curve or a dive of less than time we will make the cumulative frequency distribution of less than time. So here the scores for the class interval 0 to 10 will be less than 10. For class interval 10 to 20 it will be less than 20 and so on. Now the cumulative frequency for scores less than 10 will be 5. For less than 20 means scores 0 to 10 and 10 to 20 so it will be 5 plus 7 that is 12. Now it will be 12 plus 9, 21, 21 plus 5, 26, then 26 plus 6, 32, 32 plus 8, 40 and 40 plus 10, 50. Now the points 10, 20, 30 and so on and the upper limits of the class intervals. So let us draw the graph by taking upper limits on x-axis and cumulative frequency on y-axis like this. Now we will plot the points of ordered pairs of upper limits and cumulative frequencies corresponding to each upper limit. So our first ordered pair will be 10, 5. So let us plot the point 10, 5. So this is the required point. Now the next point is 20, 12. So it will be over here. Let us plot all the points. So we got all the points to get the curve. So this curve is less than or jive, a cumulative frequency curve of less than time. Now let us move on to cumulative frequency curve or jive of more than time. We will draw this curve for the same data. So here this course for a class interval 0 to 10 will be more than or equal to 0. For this it will be more than or equal to 10. Same way we will get all of them like this. Now here n is equal to 50. So the cumulative frequency for this will start from 50 as this course more than or equal to 0 means scores from 0 to 10, 10 to 20 and so on up to 70. So it will include all the frequencies of all the class intervals. So it will be 50. Now more than or equal to 10 means we will exclude the scores from 0 to 10. So we will exclude the frequency 5 from the cumulative frequency 50. So it will be 50 minus 5, 45. Next will be 45 minus 7 that is 38, then 38 minus 9, 29, 29 minus 5, 24, 24 minus 6, 18 and lastly 18 minus 8, 10. Now 0, 10, 20 and so on these values are the lower limits of the class intervals. So to draw the graph we will take these values on the x-axis that is the lower limits and cumulative frequency on y-axis. Here we will draw the graph. Now we will plot the points of ordered pairs, lower limits and cumulative frequency corresponding to each lower limit. So our first point will be 0, 50. So let us plot the point. So we got all the points. Now we will join them by freehand to get the graph, the median from more than oji. We already know that n is equal to 50. So n upon 2 will be equal to 25. Now we will locate n upon 2 that is 25 on the y-axis. So here we have line parallel to x-axis to cut the graph. So this point that is 38 is the median for the given data that is less than oji and more than oji on the same graph sheet. So let us draw the two graphs on the same graph sheet. So here we have drawn both the graphs that is less than oji when more than oji on the same graph sheet comes intersect. So this is the point. Now from this point we will draw up to get the median. We have learnt how to draw cumulative frequency curve or oji of less than type, cumulative frequency curve or oji of more than type and how to find out median from cumulative frequency curves. With this we finish this session. Hope you must have understood the concepts. Nice day.