CSAT: Introduction to Data Interpretation
The basic rationale behind logical reasoning K-slips okay where you did not have data being given directly is that you have to do all the hard work in terms of collecting the data and organizing it. Okay? That is the difference of L R in comparison to do something like data interpretation. In data interpretation what we see is we have a lot of pies, pie charts, bar graphs, charts, line graphs, different formats of graphs, which, where, you know you have all the data presented to you but the problem here is the data is not all that there is. In logical reasoning data was all that there was. You organize the data, see the structure, you are going to get all the answers. But here the data is already given to you. You have to then do a lot of calculations. Before we start off, okay, before you take a look at today’s sheet, I would like you to just understand a few core concepts of basics as we all call it. Some of you might be very well aware of what I am going to say right now but I still want to go through it. Just give me a couple of minutes. Okay? So one of the basic graphs that you will find or the most popular graphs that you will find is called a pie chart. Okay? It’s called a pie chart. So it looks like a pie. Get it? Basically this pie chart is supposed to go forward and help symbolify or denote 100 percentage. So that complete circle or the complete pie is supposed to go forward and give us 100 percentage of something. 100 percentage of anything means all or everything of something. Right? So you are denoting everything of something. Now this, it can be 100 percentage or this can be 100 percentage of population of a city, it can be 100 percentage of the revenue of a particular family, it can be 100 percentage of the spend of a particular department in the government. You get my point? It can be 100 percentage of anything. Right? What is the value that this 100 percentage stands for is usually not, I am repeating it, it is usually not present inside this pie chart. It will be given as a small little piece of information outside of it. So that information gives you the real value of this pie chart. Right? But why do you have a pie chart? You don’t have a pie chart to show that 100 percent can be put in a circle. That’s not the point, right? You have a pie chart because you want to go forward and then split this 100 percentage of everything of something into smaller units. So for e.g. if you are looking at a family’s income and you are using a pie chart to represent the family’s income, you will probably go forward and say, this much is by the father, this much is by the mother, this much is family inheritance, this much is bank savings. Right? Now just by depicting it like this is not going to give us any idea. I know you might have different opinions on how the family earns income, okay? I only have these four ideas, right? So coming back, I have split it into four different regions. Now, if I do not have some kind of a geometrical device, I will not be able to measure this particular region. So there are two ways in which we are helped, or we are given ideas on what the area or what the weightage of a particular region is, okay? That can be done in two ways, one is directly give you the value because whole pie chart stands for how much percentage? 100. So you directly give the value. You say that this is around 40 percent, this is around 50 percent. This is around 30 percent, this is around 20 percent but the only thing is this complete set of values should go forward and give you how much percentage? 100 percent. Obviously the guy who has given you these value does not know math, right? It’s thirty plus twenty plus forty plus fifty. How much is the percentage now? 140 percentage. So this is a bogus pie chart. Okay. This is a bogus pie chart. So I will go forward and just correct myself. I will say ok this is twenty thirty. Got it? Now does it, now does it sound fine? So all the four sectors of the pie chart or segments of the pie chart denote the 100 percentage of the pie chart, or the whole pie chart, it totals up to 100 percentage. Got it? So one method is to give you percentages. Another indirect method, okay? Something that is crooked is to go forward and give you the degree or the angle covered. We would just need to recollect the very basics of math or geometry to understand this. The circle has how many degrees inside of it? 360 degrees inside of it. So basically you are supposed to be told if segments are being made you are supposed to be told what is the measure of the angle inside these particular sectors. So it’s given degrees. So this is like 90 degrees, this is again 90, this is 60, this is 30, this is 90. These are in degrees. It will be specifically mentioned. Okay? So you will not have any ambiguity or confusion in terms of what it is, percentage or degrees. Because it will be very clearly mentioned that this is 30 percent, or this is 30 degrees. Right? The moment you get this, you are one step away from using the pie chart, because a pie chart actually cannot be used, or in most cases, it cannot be used in the degree format. You will have to convert the degree into percentage. So basically this small segment, this small segment here, which I said is 30 degrees is going to be some percentage of the complete circle’s area, right? What is a complete circle? It is 360. What portion is 30 of it? You want to get the value in percentage, multiply by 100. So 30 is what portion of 360? Multiply that by 100, you will get the percentage. The golden rule is with respect to percentages, I know you would have covered percentages by now you will have an idea you know what percentage is but the golden rule for me with respect to percentages you find a portion of what that number is to the total. So you are being asked what is 24 as a part of your sectional marks. Okay? The sectional test marks. The sectional test marks happens to be 50 marks. Okay? So what is 24 with respect to 50, as a ratio, as a fraction as a percentage. The difference here is if it’s a ratio, you will say its 24 is to 50. As a fraction you will say 24 by 50. Okay? As a percentage what you will say it’s 24 by 50, just multiply that particular result by 100. You will get your percentage value. Right? This is basically what you are doing. Same is the care here to go forward and find out what portion 30 is out of 360. You do 30 by 360 in to 100. Okay? So this is the only two way you will get a pie chart. Fine. This is with respect to pie charts.
Now if you go forward there is one more graph that is slightly important, i.e., bar graphs. So, again, this is the time that you are first introduced to graphs which are on the xy axis. Okay? Graphs which are on the xy axis. Usually in bar graphs what happens is or 99 percent of all bar graphs what happens is one axis actually denotes something constant. Okay? It’s not a value that you will keep looking at, it will be a time period or a place or a segment or a sector. So for e.g. I am saying x-axis denotes the years. So I am saying 90, 91, 92, 93, right? Your y-axis will give you values for these four years. So for e.g. y-axis stands for the dollars earned, this is a cities’ tax income. Okay? This bar graph stands for a city’s tax income. In 90, so you are looking at $100, 200, 300, you are going all the way up to 500. That’s 400 in between. You will go back and say in 90 there was only $200 earned. So you will draw a bar which is at the height of 200. 91 it went up to 400, 92 again 400, 93 it went up all the way to 500. If it’s somewhere in between, if this bar stops somewhere in between let’s say this is the height, this is the height of the bar. You will assume this is somewhere close to 350. Because that much of classification or bifurcation won’t be given for the bar. There is one small, there is one small deviation to this. It’s called stacked bar. So instead of one bar per year you will be given two bars. So for e.g. I am having one bar which is having diagonal stripes, this stands for city income because of traffic police. Dotted bar looks at city income because of liquor shops. Okay? Okay I couldn’t think of anything else. Sorry. Okay? So, 200, 90, and I have another bar put on top of my 1990’s first bar which is traffic bar which is, this is the whole concept, stacking of the bars which gives a liquor shop value. Right? So individually you look at these bars. You look at the height of these bars. Okay? So this is called a stacked bar concept. Right? So first we looked at a pie chart, then we looked at a bar graph. Okay? Slight deviation of bar graph is stacked bar and we are on to the last major category, the last major category. So I hope you have this imprint in your mind. What a bar graph stands for and what a stacked bar stands for.
The last major category that we have is a line graph. Very simple. The moment you hear graph you know that it has to be plotted on a xy-axis. Starts with zero. Line graph, I am just giving you one single line. Okay? Let’s assume these are cut equally. This is 10, this is 20, this is 30. This is let’s say the year 92, year 93, 94, it can change. The values can change for x and y. I am having a line. Okay? Which goes like this. The key points here is if you are looking at any of these years you are seeing the value in 92 is 10, the value in 93 is 20, the value in 94 does not exist. There is no value. Right? There is no value that is there for 94. It’s just dead after that. It’s not reaching 94. But if it’s better to go like this. You will say the value for 94 is something close to this, you will drop this down. It will be close to 30. So your break points, okay? Based on one of the axis on that line to the other axis is going to give you the value. Checking the value is very simple. Usually what they do, usually I am saying, 9 out of 10 cases the person who set the paper does not want to give you a pain to your brain. He will go forward and give you these break points. We call them legends. Why he gives it to you is because you will not have just one line. You will have two to three different lines explaining or showcasing different legends. So for e.g. this line graph were to stand for power generation, he would say this is power generation per year based on coal. This legend stands for nuclear power. This legend stands for hydroelectricity. Okay? Through water. And he will give you different line graphs, okay, based on these legends. You will have a triangle here, triangle here and a triangle here. This is how hydroelectricity is providing power in that city for the 3 years. You will have multiple lines. Right? Very simple. Checking a line graph can be the most easy process. The most easy process. The difficulty comes when it becomes a cumulative line graph. Okay? The difficulty arises when you are, when you come across a cumulative line graph. So, like there is a bar graph and a slight deviation called stack bar, the line graph has a very, very important but very slight deviation known as cumulative line graph. Okay? Cumulative line graph. I will just take one line to explain this to you. One line. The value here in 92 is 10, the value here in 93 is 20, the value here in 94 is 30.Okay? And it specifically mentions this is a cumulative line graph. If it’s not mentioned, what will you take it as a simple normal line graph, right? It’s specifically mentioned so please keep that in mind. It has to be specifically mentioned. You cannot go for and randomly assume this graph I want to take it as a line graph, this one is a nice cumulative line graph. Right? You will have to be told what is. If it’s not told, nothing is mentioned. Just a few lines that are plotted in a particular graph, okay? Or few points that are connected by a line and looks like a line graph, you will have to take it as a normal line graph. This is the first rule. Okay? If it is specifically mentioned as a, that this is a line graph right? But it is a cumulative line graph, special line graph, we go forward and figure out the values differently. The values that I have mentioned here, 10, 20, 30 for the years 92, 93, 94 for power through coal, okay? This is megawatts of power generated, right? In a line graph, these are the values. In a cumulative line graph, cumulative line graph the same years if this graph had to represent a cumulative line graph, it cannot be both the graphs are the same in time. Okay? If people are thinking like that, it cannot happen. Okay? So if it’s a cumulative line graph and they say it’s not a line graph go back to the cumulative line graph, you will come back and say, this particular year 92 is 10 itself, because before that the value was zero. So it’s starting from zero, it goes up to 10, so the value is 10 minus zero equal to 10. Okay? So I have written the value in black here, it is 10. Okay, I have rewritten the value. The first value is a normal line graph. The second values is a cumulative line graph. For the year 93, the value shows 20, but the previous, the previous year’s value was 10. So when I am saying it is a cumulative line graph, 20 has added. It has accumulated, the previous year’s value also to the current year’s value. So 20 minus the previous year’s value gives me the current year’s value. That’s 20 minus the previous 10. It gives me a value of 10. According to a cumulative line graph. Okay? Final year I am looking at 94. Okay? 94 the current value is 30. It has accumulated the values, so the last value is 20, it has accumulated all the values till then minus the last value, gives me the current value which is 10. So according to this cumulative line graph, 92, 93, 94 all the years the power generated through coal, that’s the example we have here right? Coal is the legend we have used, is 10, 10 and 10. The values will obviously change. If it were to be a line graph or if it were to be a cumulative line graph. If these two legends are on the same line. There is no change, the value is zero. We will look at examples like that okay. If this is on the same line so what I was trying to tell you was if this is line graph, this is 91, 92, 93. Okay 3 years. Looking at a line coming here, line coming here, okay? Line going up. So this is like 10, 20, 30. The year 94 is there. Okay in the year 94 it has come here. So, sorry, in the year 94 it has come down here, okay? In the year 92, 92 your value showcases 20. It is a cumulative line graph. We are reading a cumulative line graph. Previous value is 10. Previous value is 10. So 20 minus 10, the value here is 10. In the year 93, the value shows 20. Previous value is what? 20. So in the year 93 has any power generation happened or is there any value for 93? No, the value is zero. That’s the meaning. Sometimes, if this particular graph is showcasing growth percentage, it can even become negative. It can even become negative. Now the most comfortable way to actually show you guys graphs is when 91, 92, the years, the names or whatever it is, the sectors they have given the x-axis that is very comfortable. I have just given a very uncomfortable representation where the years is in y-axis. Usually, I am saying, 7 out of 10 graphs you’ll find this particular, this kind of value, okay, which is constant, in the x-axis. The reason is it’s more easy to visualize, or easy to view. There is no other reason for that. Okay? Even if it’s y-axis the values will anyway be the same. Okay? So you have understood line graph, you have understood cumulative line graph, right? Before which we understood a bar graph, a stacked bar, before which we understood a pie chart. Understanding these 3 graphs is more or less enough to go forward and answer 95% of your data interpretation based questions. Now the beauty is, or the only thing left is take these values and do whatever is required according to the questions. So, if you ask me how important is this in terms of getting the answer, I can tell you it’s not at all important. Because you will never get the answer by looking at this. Most of the times you’ll have to get these values, this 10, this zero and then do something with it. That is what we call calculations. So if you ask me what’s the most important step, maybe for me, its calculations? But for someone else, if you cannot get this value, obviously this becomes the most important step, because if you make a mistake in extraction, or getting the data, or what we call interpretation, you are gone. There is no point calculating anything, right?