 Hello and welcome to the session. Let us discuss the following question. Question says, the following distribution gives the daily income of 50 workers of a factory. This is the given distribution. Convert the distribution above to a less than type cumulative distribution and drives a drive. First of all, let us understand that representing a cumulative frequency distribution graphically is called cumulative frequency curves or an ojives of less than type or of more than type. So we can write representing a cumulative frequency distribution graphically is known as ojives. Now we will use this as our key idea to solve the given question. Let us now start with the solution. First of all, we will convert the given distribution to a less than type cumulative distribution. Now in the given question, we are given this distribution. This distribution gives the daily income of 50 workers of a factory. Now from this table, try to answer how many workers have income less than 120. Clearly we can see 12 workers have income less than 120. We know these are continuous class intervals and this value 120 is not included in this interval but it is included in this interval. So here we can write number of workers having income less than 120 is equal to 12. Similarly, now try to answer the question that how many workers have income less than 140. We know 140 is not included in this interval but it is included in this interval. Now clearly we can see number of workers having income less than 140 is equal to 14 plus 12. We know this income is also less than 140 and this interval also includes the number of workers having income less than 140. So total number of workers having income less than 140 is equal to 12 plus 14 that is 26. Similarly we can find number of workers having income less than 160. Now number of workers having income less than 160 is equal to 8 plus 14 plus 12 or we can say if they are equal to 26 plus 8. These workers as well as these workers have income less than 160. So we can write number of workers having income less than 160 is equal to 26 plus 8 that is 34. Now we will find out number of workers having income less than 180. It includes these workers and number of workers having income less than 160. So we can write number of workers having income less than 180 is equal to 34 plus 6 that is 40. Clearly we can see number of workers having income in the range 160 to less than 180 is equal to 6 and these workers also have the income less than 180. So we will add these two terms and we get this as number of workers having income less than 180. Now we will find out how many workers have income less than 200. They are 10 plus 40 which is further equal to 50. Clearly we can see 10 workers have income from 180 to less than 200 and 40 workers have income less than 180. So total number of workers having income less than 200 is equal to 40 plus 10 that is 50. Now this is the required less than type cumulative frequency distribution. Now to represent this data graphically we have the upper limits of the class intervals on the x-axis and these cumulative frequencies on the y-axis. Clearly we can see we have marked upper limits on the x-axis and cumulative frequency on the y-axis. You know these number of workers represent the cumulative frequency Now we will plot the points 120, 12, 140, 26, 160, 34, 180, 40, 250. On the graph to draw a no-jive we always plot the points corresponding to ordered pairs given by upper limit and cumulative frequency. Let us now plot all the points on the graph. Now this point represents 120, 12 Now we have to plot 140, 26 This point represents 140, 26 Next point is 160, 34 This point represents 160, 34 Now we have to plot 180, 40 This point represents 180, 40 Now last point is 250 So this point is 250 Now join these points by a free hand smooth curve. The curve we get is called the cumulative frequency curve or an o-jive of less than type. Remember that we can choose any convenient scale on both the x-axis. The scale may not be same on both the x-axis. Now this scale on the graph indicates that all the values between 0 to 100 are present on the x-axis. But we have not shown here as they are not required. So this is our required less than type o-jive. This complete session. Hope you understood the solution. Take care and have a nice day.