 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that calculate the median lower and upper quartile income graphically for the following data. Here the distribution is given such that the income is given in the range of 0 to 5, 5 to 10, 10 to 15 and so on till 35 to 40 dollars and the corresponding number of persons are given by 2, 6, 12, 9, 15, 5, 7, 3. First we find cumulative frequency curve. We draw one ojif by less than method that is by taking cumulative frequency on the y-axis and variable that is the upper limit x-axis. Key idea let us proceed with the solution the given distribution is as follows. Next we shall find cumulative frequency and the first entry in the cumulative frequency column will be same as that of frequency that is 2. Next will be 2 plus 6 that is 8, 8 plus 12, 20, 20 plus 9, 29, 29 plus 15, 44, 44 plus 5, 49, 49 plus 7, 56, 56 plus 3, 59. Now we will plot the graph such that we take the variable that is the upper limit on the x-axis and cumulative frequency on the y-axis. Now we will plot the points. The points are 5, 2, 8, 15, 20, 20, 29, 25, 44, 30, 49, 35, 56, 40, 59. Now we will join these points by a smooth curve. This is called the less than curve. Here for the given distribution n is given by the sum of the frequencies that is 59. We know that for continuous series median is given by the size of n by 2th item that is the size of 59 by 2th item equal to the size of 29.5th item. Now we mark the point 29.5 on y-axis and name it as a. From a, draw a line parallel to x-axis. Let it meet the ojif at point p. From p, draw a perpendicular on the x-axis and the point where this perpendicular meets the x-axis is the median. Therefore, median is equal to 20.16. Now lower quartile q1 is given by the size of n by 4th item that is the size of 59 by 4th item equal to the size of 14.75th item. Mark 14.75 on the y-axis and name it as b. From b, draw a line parallel to x-axis corresponding to y is equal to 14.75. Let it meet the ojif at point q. Draw a perpendicular from q on the x-axis and the point where this perpendicular meets the x-axis is the lower quartile given by 12.81. Therefore, lower quartile q1 is equal to 12.81. We know that upper quartile q3 is given by the size of 3n by 4th item that is the size of 3n259 by 4th item which is equal to the size of 44.25th item. We mark the point 44.25 on the y-axis and name it as c. Now draw a line parallel to x-axis corresponding to y is equal to 44.25. Let it meet the ojif at point r. From r, draw a perpendicular on the x-axis and the point where this perpendicular meets the x-axis is the value of upper quartile that is 25.25. Therefore, upper quartile q3 is equal to 25.25. Hence, median is equal to 20.16 lower quartile q1 is equal to 12.81 and upper quartile q3 is equal to 25.25 which is the required answer. This completes our session. Hope you enjoyed this session.