 Hello and welcome to the session. In this session we discuss the following question which says draw a histogram to represent the falling data in which we have the class interval 0 to 10 has frequency 10, class interval 10 to 15 has frequency 7, class interval 15 to 25 has frequency 8, class interval 25 to 32 has frequency 14, class interval 32 to 40 has frequency 24. Now we move on to the solution. We need to draw histogram that will represent this data. As you can see in the given table, the class intervals have different widths like in the first class interval, the width of the class interval is 10, in the next one is 5, in the next it's 10, in the next one it's 7 and in the next one it's 8. So, here the width of the class interval is varying. Now we will find the adjusted frequencies of the given class intervals. Now first class interval is 0 to 10, frequency is 10, class size would be 10. Next class interval is 10 to 15, frequency given is 7, class size is 5. Next is 15 to 25, frequency given is 8, class size would be 10. Then next class interval is 25 to 32, frequency is 14, class size is 7. Then next one is 32 to 40, frequency given is 24, class size is 8. Now we will find out the adjusted frequencies for all the class intervals. For this, first we need to select a class interval with the minimum class size. Like in this case, you can see that the minimum class size is 5 and that is for the interval 10 to 15. Now we will adjust the frequencies to be proportionate to the class size 5 and the adjusted frequency is given by frequency upon the class size multiplied by the minimum class size that is 5. So for the class interval 0 to 10, let's find out the adjusted frequency. It would be the frequency 10 upon the class size 10 into the minimum class size 5 and this would be equal to 5. For the next interval 10 to 15, adjusted frequency is given by frequency that is 7 upon the class size that is 5 into the minimum class size that is 5 and so this is equal to 7. Now the adjusted frequency for the next interval that is 15 to 25 is given by frequency 8 upon the class size 10 multiplied by the minimum class size 5 and so this is equal to 4. Now for the next interval 25 to 32, adjusted frequency is given by the frequency 14 upon the class size 7 into the minimum class size that is 5 and so this is equal to 10. For the interval 32 to 40, the adjusted frequency is given by frequency 24 upon the class size 8 multiplied by the minimum class size 5 and this would be equal to 15. So we have got the adjusted frequencies for all the intervals. Now we can draw histogram. We have represented the class intervals on the horizontal axis and the scale that we have taken on the horizontal axis is given as 1 centimeters is equal to 5 units and on the vertical axis. We have plotted the adjusted frequencies and the scale that we have taken on the vertical axis is 1 centimeter equal to 5 units. Now on this graph, we will draw rectangles of width equal to the class size and length of the rectangles would be equal to the adjusted frequencies for the given class intervals. So first consider the class interval 0 to 10, its class size is 10 so we will make a rectangle of width 10 and the length of the rectangle would be given by 5. So this rectangle represents the class interval 0 to 10 with adjusted frequency 5. In the same way for the next class interval 10 to 15, we will draw a rectangle of width 5 and length 7. This rectangle represents the class interval 10 to 15 with adjusted frequency 7. Next we have the class interval 15 to 25 with class size 10 and adjusted frequency 4. This rectangle shows the class interval 15 to 25 with adjusted frequency 4. Next is 25 to 32 class intervals with class size 7 and adjusted frequency 10. So for this we will make a rectangle of width 7 units and length 10 units. This rectangle represents the class interval 25 to 32 and adjusted frequency 10. Then we have the class interval 32 to 40 with class size 8 and adjusted frequency 15. This rectangle shows the class interval 32 to 40 and adjusted frequency 15. This is the histogram which represents the data given to us. So this completes the session. Hope you have understood the solution for this question.