Hi, friends, we will start now with a new module which is based on bar diagram. It is most common type of diagram which is used in practice. They are called the one dimensional because only the length of the bar matters but not the width of the bar is mattered.

Here, what are the types of dimensional, one dimensional bar diagrams. You have nothing but what a horizontal, then vertical, then multiple and then the sub-divided bar diagram.

Now, we start with the first one Horizontal Bar Diagram. For which type of data it is used, it is used for the qualitative data or data related to space or area. This is example of horizontal bar diagram. Now the next one that is vertical bar diagram. For which type of data it is used. That is for quantitative data and here the most of the data represented by the vertical bar diagram. This is what, an example of Vertical Bar Diagram. The next one that is Multiple Bar Diagram or a Joint Bar Diagram or a Group Bar Diagram. So, here obviously it is used to represent two or more numbers related to each group. Let’s take simple example, maximum and minimum two or more numbers for different cities for each group. And the second one is yes, that is income and expenditure of different families. Again now let us take a simple example of this. Year wise we have been given an income and expenditure two numbers. Just draw the, you know how to draw this. So, years on the x-axis and income and expenditure on y-axis. So, expenditure and income is drawn in 2001, that is 4000 is the income and for the same year my expenditure is about 2000, so the second bar. So, that is nothing but grey. And similarly 2002 also that we have 8000 and 6000 and for 2003 we have income of that is 10,000 and your expenditure is nothing but 4000. Now, the next one, that is 4^{th} one, sub-divided bar diagram. Bar is divided into what a sub-divided group. So, when total and the components of a group are to be represented then such bar diagram is called as what sub-divided bar diagram. You know that total students of a different division and the number of boys and girls in the each division. Now, let us take a simple example. We have been given what, a subject wise that is college wise and the subject wise students here. Now, we are going to take a college on the x-axis and on the y-axis we are going to take number of students, three subjects that is maths, science and economics. Just first we have to take for the college A, 700 students are there total. Now we are going to divide that, the mathematics we have about 300 students, for stats we have 250 students and for economics we have about 150 students. And so on for the college B same that is we have to draw and for the college C also we have to consider the same way, so, the total is 350 and the maths students that is 200 and then we have stats students that is 100 and the remaining students for the economy that is nothing but about 50. Now, the next one, that is what, here what is important point, in this diagram the bar is sub-divided into various parts in proportional to the, what a given value. The next second point, each part is shaded differently to distinguish it from what, others. Now, the next one that is Percentage Bar. Here, the same concept you know but we are going to divide in terms of percentage, so when such diagrams are prepared the length of the bar is kept equal to 100 and segments are cut in bars to replace components or percentage of an aggregate. Let us take simple example family A and family B, we have been given a components expenditure food, clothing, rent, educations, recreations and miscellaneous. Now, family A raised to the 100, now 58, for the food 58. For the clothing that is 58 plus 10, so 58 plus 10, so we have to raise to nothing but what 68 and so on 68 plus 12, so that is 80. 80 plus 6, 86 and 86 plus 4 is to 90 and 90 plus 10 so that is nothing but 100. For the family B also we have to consider same way, raised to the 100 and then for the food that is 54 percentage, 54 plus 8 that is 62 and from that 77 plus 5, 82, 82 plus 10 is 92 and 92 plus 8 that is 100. So, Percentage Bar diagram.

Now, we have Two Dimensional Bar diagram. Obviously here length and the width of the bar diagram are important for the Two Dimensional Bar Diagram. In such case the area of the bars represent the what, given data. It is also called area diagram or a surface diagram. The different types of that is Two Dimensional Bar diagrams that includes pie chart, rectangle, square and the diagrams. Most common used is the pie diagram or a pie chart. Let us take a simple example of a pie chart. Now, as the name suggests a circle is used to represent the given data. A circle is divided into number of sectors representing different components of a variable. The area of such sector is proportional to the value of the components. Pie diagram is used for comparing the different components and their relations to the total. Multiple bar diagram can also be used but pie diagram is better you know when more than two variables are there, when more than two components are there. In this case a component value are converted into more than two angles measured in degree. What is the formula for that, yes you know that angle is nothing but what, value of component upon the total value into 360 degree. Now, let us take a simple example, how to draw a pie diagram? You already know this concept just I will take you brief idea of that. That is 40 for food, we have a 40% expenditure that is 40 upon total is 100, so 40 upto 100 into 360, we get what that is nothing but what, we get angle as 144 angle. So, we have to draw angle of 144 from here, now for the clothing is same we have to draw the angle of 72 degree and for the house rent again we have to draw 72 degree angle, for the education your angle is 36 degree and for the other expenses your angle is nothing but what is a 36 degree and this is what pie diagram is all about.

Now, MCQs based on all these concepts. The first one, the vertical bar diagram is applicable when, what, yes, your answer in this case is b, a data or a quantitative nature. The second one, divided bar chart is considered for what? Yes, the (6:47) that is your answer in this case is d, a and b, comparing the different components of variable and the relation of the different components to the total. That is the main concept for the divided pie chart. Next one, that is cost of sugar in a month under the heads raw materials and labour, direct productions and others were 12, 20, 35 and 23 units respectively. What is the difference between the central angles for the largest and smallest components of the cost of sugar? Very simple, my dear students, what is the largest one here, 35, now get the total of all these things first. So, 12 plus 20 plus 35 plus 23, we get over 90 units. Largest unit is what, 35, 35 upon 90 into 360, so 140. So, the smallest one is, which one, it is 12 so 12 upon 90 into 360, 48. Get the difference of that 140 – 48, 92. Yes, my dear students the answer is D. Next one, in order to compare the two related series, yes, my dear students, what we require the answer is c, that is a or b. The next one, that is question number 5. A pie diagram is used to represent the following data. Now, central angles in the pie diagram corresponding to income tax and wealth tax. Income tax, just see 240, first write the total. What will be the total? Total is nothing but what, 720. So, 240 upon 720, your angle is 120. And for the wealth tax, where is wealth, how much the wealth? So, 180 upon 720 into 360, your answer is nothing but what, 90 degree here. So, your answer in this case is A.

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