 Hello and welcome to the session. In this session we will discuss graphs. Graphical representation of data is easier to understand. So we make use of graphs to represent the data. Especially when we need to show some trend or comparison. Now we shall discuss different types of graphs. First we have a bar graph. A bar graph is used to show comparison among categories. It consists of two or more parallel, vertical or horizontal bars or you can say rectangles. This is a bar graph which shows the performance of a class. So according to this we have, that 15 students got the first division, 5 students got second division and 10 students got third division in a class. So this bar graph shows the comparison of the performance of the students. As you can see in this bar graph we have parallel vertical rectangles. In the bar graph we can also have double bars. This is a bar graph which has double bars. This gives the comparison of the performance of the class in two years, that is in the year 1995 and in the year 1996. The bar which is shaded shows the performance of the class in the year 1995 and which is not shaded shows the performance of the class in the year 1996. It shows that in the year 1996 15 students got the first division and in the year 1995 10 students got the first division. In the year 1996 5 students got the second division and 10 students got second division in the year 1995. In the same way in the year 1996 10 students got the third division and 20 students got the third division in the year 1995. So this is how we can show comparison among different categories using the bar graphs. Next type of graph that we need to discuss is a pie graph or a circle graph. A pie graph is used to compare parts of a whole. This pie graph or you can say the circle graph shows the percentage of people eating different kinds of fruits. So according to this we have that 25% of the total people prefer eating apple, 35% of the total people prefer eating grapes and 40% of the total people prefer eating banana. Next is a histogram. A histogram is a bar graph that shows data in intervals. Consider this table which shows different age groups and the number of persons falling under each age group. Now we have taken the age group along the x-axis and the number of persons along the y-axis to represent this data using histogram. As we know the histogram shows the data in intervals. So according to this histogram we have that the number of people falling under the age group 20 to 30 is given by this rectangular bar which shows that there are 15 people. Then this rectangular bar shows that there are 10 people falling under the age group 30 to 40 and the number of people falling under the age group 40 to 50 are 5 which is shown by this rectangular bar. This rectangular bar shows that there are 20 people falling under the age group 50 to 60 and according to this rectangular bar we have that the number of people falling under the age group 60 to 70 are 10 and this jack line that you can see on the horizontal axis shows that we are not showing the numbers between 0 and 20. As you can see there are no gaps between the bars because there are no gaps between the bars also. Next is a line graph. It displays data that changes continuously over periods of time. This is the line graph which shows the early sales figure for a manufacturing company. According to this we have that the sales of the company in the year 2002 is given as rupees 4 crores which rose to rupees 8 crores in the year 2003. Then in the next year that is in the year 2004 it came down to rupees 2 crores. In the year 2005 the sales rose to rupees 6 crores and in the year 2006 the sales rose to rupees 6 crores again. That is the sales remained constant for a year. This is how we represent the data using a line graph. In this way I have taken the x axis or the horizontal axis as the years and on the y axis we have represented the sales of the company. Next we shall discuss linear graphs. A linear graph is basically a line graph which is a whole unbroken line. For such lines we need to locate some points on the graph sheet. Location of a point on a graph sheet is given by the x coordinate and the y coordinate. On the graph sheet we draw the x axis and the y axis. So as you can see we have drawn the x axis and the y axis. Let's try to locate the point 1,3 on the graph paper. In this this 1 is the x coordinate of the point and 3 is the y coordinate of the point. To locate the point 1,3 we first move one unit to the right of the origin since we have that the x coordinate is 1 so we will move just one unit to the right of the origin that is to this point. Now from here we will move 3 units above the x axis that is to this point since we have that the y coordinate is 3. So this point that we have got is 1,3. This is how we locate the point on the graph sheet. In the same way we locate the point 2,2 so we get this is the point 2,2. Then we locate the point 3,1. This would be the point 3,1. Let's name these points as A, B, C. Now we join these 3 points ABC. As you can see on joining these 3 points we get a line that is the graph obtained by joining these points is a line. So this graph is a linear graph. Now let's discuss some applications. The relation between dependent variable, independent variable is shown through a graph. Let's see how we can do this. This table shows the number of apples and their cost. Let's draw a graph for this table by taking a suitable scale and the scale that we have taken on the x axis is 1 unit is equal to 1 apple and on y axis the scale that we have taken is 1 unit is equal to rupees 5. Now in this case the number of apples is an independent variable or we can also call it control variable and the cost of the apples is the dependent variable. Let's show the relation using a graph. We need to plot the points 1,5, 2,10, 3,15, 4,20 and 5,25. Let's plot these points one by one. So as you can see we have plotted these points. Now we shall join these points to get the graph. So as you can see that the graph is a line. So this is how we can show relationship between dependent variable and the independent variable using a graph. This completes this session. Hope you have understood the concept of graphs.