 Hello and welcome to the session. In this session we will discuss how to sketch and read circle graphs. Now, a circle graph or a pile frame is a graph in the form of a circle that is divided into sectors with each sector representing a part of a set of data. Now, seeing the following circle graph, it represents the data distribution of favorite ice cream of the students in a class where this circle is divided into three sectors. This red sector represents percentage of students who like chocolate ice cream. This blue sector represents percentage of students who like strawberry ice cream and this green sector represents percentage of students who like vanilla ice cream. So, we can read that in the class, 55% of the students like chocolate ice cream, 30% of the students like strawberry ice cream and 15% of the students like vanilla ice cream. Also, you must note that the sum of percentage on a circle graph will always equal to 100%. As you can see, 55% plus 30% plus 15% is equal to 100%. Now, let us see how to sketch circle graphs. The data given to be represented in a circle graph can be either in percentage or in frequency distribution. Now, let us see how to sketch circle graph when we are given frequency distribution. Now, consider an example. Now, this table shows the results of a survey to note the number of people having no pet, one pet, two pets and three or more pets. In the first column, we are given the category of pets and in second column, we are given the frequency for each category. Now, we will represent this data in a circle graph. In step one, we will find the total number of people surveyed that will be equal to sum of all the frequencies that is 10 plus 8 plus 4 plus 2 which is equal to 24. In step two, to make a circle graph, we will find the appropriate angle measure for each sector such that sum of angles of all the sectors is 360 degrees. So, to find the angle measure of each sector, we write each group of people as a fraction of all the people and multiply it by 360 degrees. So, angle measure for more pet is given by number of people in this category that is 10 upon total number of people that is 24 into 360 degrees. And on calculating, this is equal to 150 degrees. Similarly, for one pet, angle measure is 8 upon 24 into 360 degrees that is equal to 120 degrees. Then for two pets, it is 4 upon 24 into 360 degrees that is equal to 60 degrees and for three or more pets, it is 2 upon 24 into 360 degrees and on calculating, this is equal to 30 degrees. Now, here we see that 150 degrees plus 120 degrees plus 60 degrees plus 30 degrees is equal to 360 degrees. Now, in the next step, we will draw the circle graph using protractor. First we draw the circle. Now, here we have drawn the circle. Now, we have found the degree measure for category no pets and it is 150 degrees. So, here we use a protractor to draw the angle measuring 150 degrees and we label this sector with category and frequency. Here the category is no pet and frequency is 10. Similarly, we draw other sectors and we obtain the circle graph. We also give suitable writer to the circle graph that is number of pets. Now, in a circle graph, 360 degrees represents the total frequency. So, 360 degrees upon total frequency will represent one frequency. Now, in this example, 360 degrees represents 24 people. So, 360 degrees upon total frequency that is 24 represents one frequency that is one person. Now, 360 degrees upon 24 is equal to 15 degrees. So, 15 degrees represents one person on the circle graph. Now, let us see how to make circle graph when the data is given in form of percentage. Now, here we have given this data in percentage form. Here the first column represents favorites ice cream and the second column represents the percentage of students for particular category. And we have to rate the circle graph for this data. We will directly find the angle measure for each category by multiplying each percentage by 360 degrees. Now, for chocolate flavor, angle measure will be 55% of 360 degrees. And I am calculating this is equal to 198 degrees that is 55 upon 100 into 360 degrees which is equal to 198 degrees. Similarly, we have found the angle measure for each category that is the angle measure for each sector. Now, to make it circle graph, we will use the protractor and label it as we had shown in the earlier example. Thus, we get the following circle graph for the given data. And here you can see angle measure for blue sector is 108 degrees. And this blue sector represents the 30% of students like strawberry flavor, 15% of students like vanilla flavor and 55% of students like chocolate flavor. Now, let us discuss how to interpret the circle graphs. Suppose 40 students were surveyed to know the favorite ice cream flavor. The data collected is represented in the following circle graph. From this representation that is from this circle graph, let us find which is the most preferred ice cream. Now, to know the most favorite ice cream, we look at the circle graph and we see that highest percentage belongs to the red sector representing chocolate ice cream. So, most preferred ice cream is chocolate. Now, let us find that how many students like strawberry ice cream. Now, from this graph you can see that total number of students surveyed is 40 and 30% of students prefer strawberry ice cream. So, number of students who like strawberry ice cream is equal to 30% of 40 that is equal to 30 upon 100 into 40 which is equal to 1200 upon 100 that is equal to 12. So, 12 students like strawberry ice cream. Thus, we can interpret the results from the circle graph. So, in this session we have learnt how to sketch and read circle graphs and this completes our session. Hope you all have enjoyed the session.