 Hello and welcome to the session. In this session we will discuss circle graph or pie chart. We can represent the data using the circle graph or the pie chart. A circle graph shows the relationship between a whole and its part. Circle graph is also called a pie chart. Here we divide the whole circle into sectors and the size of each sector is proportional to the information that it represents. This pie chart shows the survey done to find the type of music that a certain group of people in a city liked. So according to this we have that 40% of the total people like light music, 20% of the total people like semi-classical music and 10% of the total people like classical music also 30% of the total people like folk music. Now let us discuss drawing pie charts. To draw a pie chart for given data we should first find out the central angle for the sector and that would be the fraction of 360 degrees. Consider this data which shows the percentage of students who prefer taking apple that is 25% students prefer taking apple, 25% students prefer taking grapes and 50% students prefer taking orange. Now we shall draw a pie chart for this particular data. We know that the total angle at the center of a circle is 360 degrees. So obviously the central angle for the sectors will be the fraction of 360 degrees. So first let's find out the fraction of 360 degrees for each root or you can say let's find out the central angle for each sector. Now we can express this percentage in fractions as 25 upon 100 and this is equal to 1 upon 4 and for grapes also we have 25 upon 100 which is equal to 1 upon 4 for orange we have 50 upon 100 and that is equal to 1 upon 2. Now the central angle or you can say the fraction of 360 degrees is given by 1 upon 4 of 360 degrees and this is equal to 90 degrees 1 upon 4 of 360 degrees is equal to 90 degrees and 1 upon 2 of 360 degrees is 180 degrees. So we have got the central angle for each sector. Now to draw a pie chart we draw a circle with any convenient radius and we mark its center as O and the radius as OA. Now we have the angle of the sector for apple is 90 degrees. So we use the protractor to draw angle AOB equal to 90 degrees. So we have drawn the angle AOB equal to 90 degrees. Now in the same way we will mark the other sectors that is we make an angle of 90 degree and 180 degrees for the sectors of grapes and orange. So we have done that also we have marked the angles of 90 degrees and 180 degrees. Now this portion shows the apple, this portion shows the grapes and this portion shows the orange. So this is how we draw a pie chart for any given data. Now we discuss chance and probability. We know that there are certain experiments whose outcomes have an equal chance of occurring. Now let's define a random experiment. A random experiment is one whose outcome cannot be predicted exactly in advance. Like we say tossing a coin is a random experiment. Since we don't know that when we toss a coin we will get a head or a tail. Next we discuss equally lightly outcomes. The outcomes of an experiment are equally lightly if each has the same chance of occurring. When we toss a coin we either get a head or a tail. Both these outcomes head or tail are equally lightly outcomes. Next we have each outcome of an experiment or a collection of outcomes make an event. So in the experiment of tossing the coin getting a head is an event and getting a tail is also an event. So these are the two events. Now we discuss chance and probability related to real life. The use of probability is made in various cases in real life like it can be used to find characteristics of a large group by using a small part of the group and also it has one important use that is meteorological department depicts weather by observing trends from the data over many years in the past. So this completes the session. Hope you have understood the pie chart or the circle graph and also the concept of chance and probability.