 Hello and welcome to the session. In this session, we will discuss a question which says that study the histogram carefully and answer the given questions. And in this, the following histogram is given to us in which 800 square kilometers and the corresponding number of countries are given to us. And by observing the given histogram, we have to answer these questions. First one is, how many countries have an area less than 600 square kilometers? Second is, what percent of countries have an area greater than equal to 200 square kilometers and less than 800 square kilometers? And the third part is, how likely is it that any given country will have an area greater than equal to 800 square kilometers? Explained. Now before starting the solution of this question, you should know a result. And that is, in a histogram, the bars are raised to the height of the frequency of the class interval. Now here, suppose the first bar represents the class interval 0 to 10 and we have raised this bar to 20. This means, for the class interval 0 to 10, the frequency is 20. So this result will work out as a key idea for solving out the given question. And now, we will start with the solution. Now in this question, we are given a histogram. Let us first study the histogram. Now in the given histogram, on the horizontal axis, we are given the area of the countries in square kilometers and the area is divided in equal class intervals. And on the vertical axis, we are given the number of countries having the given area. Now according to the key idea, in a histogram, the bars are raised to the height of the frequency of the class interval. Now here, in the given histogram, you can see that the first bar covers the interval 0 to 200 and is raised to the height of 21. That there are 21 countries having an area less than 200 square kilometers. Now the second bar is raised to the height of 9. It means that there are 9 countries whose area is greater than equal to 200 square kilometers and less than 400 square kilometers. Now the third bar is raised to the height of 10, which means 10 countries have an area greater than equal to 400 square kilometers and less than 600 square kilometers. Now the fourth bar is raised to the height of 6, which means 6 countries have an area greater than equal to 600 square kilometers and less than 800 square kilometers. Then the next bar is raised to the height of 1, which means there is only one country whose area is greater than equal to 800 square kilometers and less than 1000 square kilometers. Now the last bar is raised to the height of 3, which means there are 3 countries whose area is greater than equal to 1000 square kilometers and less than 1200 square kilometers. Now after studying the histogram, we will answer these questions. The first one is how many countries have an area less than 600 square kilometers. Now from the histogram, we see that from 0 to 600, there are 3 class intervals that are from 0 to 200, then from 200 to 400 and then from 400 to 600. And the frequency of each bar is known to us and here the frequency gives us the number of countries. Now for finding out the number of countries whose area is less than 600 square kilometers, we have drawn a table. In the column 1, we will write the area in square kilometers and in the column 2, we will write the number of countries. Now from the histogram, for these 3 class intervals, we will write the corresponding frequencies, which means the corresponding number of countries for the given area in square kilometers. Now for the interval 0 to 200, the frequency is 21, that is for the area in square kilometers, which is from 0 to 200. We have the number of countries is equal to 21, then for the interval 200 to 400, the frequency is 9 that is the number of countries is 9. So we will write 9 here, then for the next interval that is 400 to 600, the frequency is for the interval 400 to 600, we have written the number of countries that is 10. Now the number of countries having an area less than which square kilometers is equal to, now we will take the sum of 21, 9 and 10, which is equal to 40. So the number of countries having an area less than 600 square kilometers is 40. Now let us start with the second part, which is what percent of countries have an area greater than equal to 200 square kilometers and less than 800 square kilometers. Now here we can see from the histogram that the second, third and fourth bars covers an area which is greater than equal to 200 square kilometers and less than 800 square kilometers. Now the second, third and fourth bars are raised to the height of 9, 10 and 6 respectively, therefore the number of countries having an area greater than equal to 200 square kilometers and less than 200 square kilometers is 9 plus 10 plus 6, which is equal to 25. So you can see that the first, second, third, fourth, fifth and sixth bars is straight to the height of 21, 9, 10, 6 respectively. Now from these frequencies we can find out the total number of countries, so the total number of countries is equal to 21 plus 9 plus 10 plus 6 plus 1 plus 3, which is equal to, so the required percentage is equal to 25 upon 50 into 100, which is equal to 50 percent. It is asked how likely is it that any given country will have an area greater than equal to 800 square kilometers. Now from the graph that is from the histogram we can see that the last two bars cover the area greater than 800 square kilometers in which the second last bar is having the frequency equal to 1 and the last bar has the frequency of Now number of countries having an area greater than equal to with square kilometers is equal to 1 plus 3, that is equal to 4. So it is not very likely that any given country will have an area equal to square kilometers. So only 4 out of the three countries has an area equal to square kilometers. We should have the given question and that's all for this session. Hope you all have enjoyed this session.