Lecture 08

追加: 2026-05-07

[00:00:01][music] [music] A very good day to dear learners. Today I welcome you to this new session in which I'll be talking about graphical presentation of data. So so far you must have seen me uh in this week that when we talked about organization of data hands-on experience regarding organization of data. So today I'm going to start with how are you going to represent data graphically. So let's have a overview of this particular session. So by the end of the session you'll be able to understand what is the objective behind graphical representation. Why do we use that in statistics or in any other discipline?

[00:00:58]And then moreover, you'll be also able to explain what are the different types of graphical representation and as well as comprehend what is the uh basic rule behind it, general rules of graphical representation and what principles are we to follow for effective graphical presentations. Okay. So let's begin.

[00:01:20]So if we talk about graphical uh representation of data now we have to understand see numerical data is so complex and it is so difficult to interpret and understand for example if if I just show you the marks just right now on the slide right so for you to just visualize think about the marks and the frequency distribution it will take a it will take time it's definitely that our eyes has to accommodate with such uh vast amount of information so basically graphical ical repetition representation is a form in which we are making visual uh visually we are making the data very appealing in the form of charts diagrams and graph so it's converting the raw tabulated data to easy to understand picture form right which also shows pattern it also shows comparisons and different relationships as well so graphical uh representation is the visual display and it is used in many academic and professional discipline. So mostly most widely it is being used in medicine, mathematics, sciences and social sciences. And moreover if we also find that when we are presenting the data graphically what it what it is doing it is helping us to quantify to sort out and present data which is understandable to a large variety of audience. No matter what the audience different learning styles are, they're able to understand by just by showing showcasing the data. Now see this is an example I took from NCERT book. Now if I show you this data which is um about the average monthly temperature and rainfall in Delhi. So for you if I ask which month has the highest rainfall or which month has the highest temperature. So it will take time. It's definitely we are humans. it will take us time to look at the data you know and even the data is uh in is in decimals we have to understand okay so let me compare which month has the uh the least amount and the highest amount it will take time but the moment I show you this now what is this the moment you see this you're not even looking at the figure it's just that yes this month has the highest uh um rainfall or highest temperatures here so we can see right here and in fact In this the both the bar graph and the line graph are simultaneously being shown and this actually tells us that yes two variables can also be visualized and it can be represented as well.

[00:03:50]So if you look into the objective of graphical representation, so of course simplification to simplify such a complex detailed data, you're reducing large scattered numerical data into a simple meaningful form which is uh understandable and which is self-explanatory and anybody can look at it. Yes, the June has the highest rainfall and least is in Feb, right? Just by looking at the uh the graph. Moreover, even the clarity to make data easy at a glance. So you can see like pie chart the moment you see it the different type of juices are given.

[00:04:28]So you know the consumption is more of tap water. I mean it's so easy. So it is easy the clear the the information is also very clearly represented. Moreover, it also helps in comparison by it enables quick comparison between groups.

[00:04:43]So graphs helps to compare different sets of data side by side. So see here the the number of line graphs it's a it is helping us to compare humanities with science with commerce right what is the past percentage of students so visuals they eliminate confusions and they make patterns very clear and very you know visual very appealing also moreover it also tells us about trend setting what is the trend so the graph shows how the data is behaving over time and it highlights the growth Even if there is a a rise or the decline or any kind of a seasonal variation just like we saw in the previous graph and even in this line graph how the rainfall is varying right where it is um um rising where is this where it is highest where why is it declining and what what is the seasonal variation. So mostly you find yes in weather report in geography we are using these kind of trend analysis also in business also you know we see the rise of the demand uh and supply of the product as well then of course not to mention the attractiveness how the moment that you see uh visuals it's so engaging you know so and makes the lesson all the more interesting and of course it also helps in decision making so once you showcase the data visually so what is happening and the and and the part where you are really particular about your data it should be very well presented it will help all the the future researchers the manager the policy makers to basically take decision based on this um particular data which has been showcased so here see by looking at the population this is the population growth over time so over a decade and we can see that how the countries have been arranged so just by visualizing it lot of policy makers and the researchers and the business decisions can be made by looking at it.

[00:06:37]Now coming to the part where we'll be looking into the different types of graphical uh presentations. So first is the bar graph which represents the rectangular bars of equal width with length which is proportion to the values right and it is of course best used for comparison. So if you have even three data here you can easily place them side by side and you can compare it just by looking at it. For example, the population in France can be easily compared with this bar graph. Okay, with different colors you can show. And here of course types of sport is there. This is vertical bar graph and this is horizontal bar graph. You can either place it vertical or horizontal. Okay.

[00:07:19]Then comes histogram. That is another type of uh bar graph for continuous frequency distribution. So where the class intervals are shown and histogram is a visual you can say presentation used to summarize discrete or continuous data and it shows the frequency distribution of continuous data mostly.

[00:07:38]So you see here the intervals are there.

[00:07:40]This is the class interval of the bin also and here of course there is no gaps here and the data is arranged with equal class interval and this shows at the different uh data. For example, here it is showing the salaries of employees from grade 0 to 10 to so on u,000 dollar. Right? So this is where the data is also being showcased.

[00:08:04]Now a question should come in your mind.

[00:08:06]What is the difference between a bar graph and histogram? They both almost look alike but there yes there is a difference. If you look at bar graph it represents categorical data. Right? So this is a bar graph. Categorical data is present here. And here there is a uh it histogram represents numerical data. It could be discrete or continuous data. So no spaces are here. Sorry spaces are here in bar graph but no spaces will be in the histogram. And uh and in bar graph equal space between two consecutive bars. Even the spacing is equal. Remember that. Okay. And the data can be arranged in any order. Right? But here the orderly arrangement is necessary. So data has to be arranged in order of the range and xaxis can represent anything in bar graph but here x-axis should represent only continuous data that is in terms of numbers.

[00:09:00]Now now this is the chart. Now you can see even this um in this particular figure these are the bin class interval is being present here no gaps and you have the x-axis which shows frequency and this uh y-axis which is showing the frequency and the x-axis which is showing the class intervals. So this is how a bar graph and a histogram will look like. Right?

[00:09:25]Now if you move forward there's another kind of um visual representation in the form of frequency polygon. Now a line graph which is connecting the midpoints of the class interval in a frequency distribution. It helps to compare basically two distributions on the same graph. Right? So you can see here if you're comparing the midpoint and the midpoint is attached to the x-axis right and this forms from zero according depending on the data that is being presented here. So you see that this is through line segments we are attaching this and we are making it into a polygon. So frequency polygons are line graphs basically which are representing a continuous data sets frequency distribution and we can get it by dividing the data into intervals or bins and u it shows us basically the overall pattern you can say of uh data distribution as well and of course it's being used in many different fields like uh economics and it is used in statistics and so on.

[00:10:29]We also find that um the if you look at the line graph the advantages what do you find that it is very easy to interpret like we can see that the information is very easy to interpret and you know it highlights the pattern the trends and it can also display a very large uh data set and also it can detect any outliers any kind of uh unusual data point can also be detected through this particular Okay.

[00:11:00]So what is the difference between histogram and frequency polygon? So if you look at the histogram, histogram usually display data using adjacent bars.

[00:11:09]Sorry.

[00:11:12]Whereas frequency polygon represents the very same data which is connected with straight lines. Okay.

[00:11:20]So histograms are mainly used for continuous data with frequency polygon can present both continuous and discrete data. Now if you look at the distribution shape of histogram the overall distribution shape of data the frequency polygon you can say that it only shows the trends and patterns across the interval. And of course in a histogram you can see the width right you can see the width of the bars but here uh the class interval is not that much it's not at all visible it's only the midpoints that are visible you don't know the width of the class interval so only it is plotted in in the form of points the midpoints and it is connected through line segments okay now let's move forward another visual representation is through the pie chart okay this is personally speaking this is one of my favorite representation it is you can make It's so colorful and the data is so lively and it's so appealing when you look at a pie chart. So it's a circular chart which is cut into different slices right and uh of course uh and the thing is that here the data is presented in the form of the percentage. So it is uh you can say the weightage or you can that the circular figure which is the weightage which is given to the proportion of data. So you know the angle of the entire circle is 360° right? If you look at the circle, the angle is 360°, right? And uh which is also converted into percentage. So for basically for um 36° it would be uh 10% for and 3.6° it would be 1%.

[00:13:00]Okay, that's how we do. And you have to of course calculate in percentages. when we'll do the hands-on experience. I'll tell you how to make the pie chart. So here of course whatever for example this is recommended diet and according to the legends the different diets uh are given here and the percentages calculated and equally the according to the percentage the pie chart is being distributed.

[00:13:23]So all the complete data will not exceed um 360°. Remember that. Okay.

[00:13:30]Now comes a line graph. So a graph that uses points to connected by lines to present any change over time. Okay, that is known as line graph. Of course, this is also showing trends and time series data. You can see here. So line graph or line chart which are used basically used to represent uh um quantitative uh data which is collected over a specific period of time. So you see the x usually has the time period. Okay. and um and any quantity that is measured is on on the y-axis and the line graph actually gives the clear picture of anything that is declining anything that is being increasing. So a simple line graph would be in the form that you see here right here and uh right. So this is a simple line graph which is showing you the uh the produced sales. Okay.

[00:14:29]Then um after the simple line graph we have the compound um the multiple line graph in the form of more than two that you can see in this figure and then comes the this is the uh multiple line graph sorry multiple line graph and this is the compound life graph. So you the more the data that is presented on a line uh graph you can easily see like for example like drought here four conditions four uh in fact five conditions are given of drought here in this by different colors also. So you see how appealing it is that that how the line graph it shows trends and time series also and it is easily comparable as well. Okay.

[00:15:13]Now coming to cumulative frequency curve which is also known as ojive right so a line graph which shows basically the cumulative frequency now once we'll do the hands-on experience you'll be able to calculate the cumulative frequency I think we did that also and how we're going to plot on that that will be in my subsequent lecture so a graphical representation of cumulative distribution is called oi which is a curve right so here it is joined by a freehand so basically al it also helps to find the median, it also helps to find the quartile and um even the percentile through this particular data.

[00:15:51]So if you look at look into the cumulative uh frequency og it is a line graph that plots cumulative frequency showing the number of data points that are below a certain value and typically it's the upper boundary of a class interval and a and a cumulative frequency polygon if you remember is also a line graph uh of cumulative frequency but it is constructed using the midpoints of the class and the connecting points are formed with the uh line segments. So there we find that the only difference is that that cumulative frequency polygon is contained is connected by line segment and but the curve is by through a free hand. So it's basically a very smooth curve. Next now the next type of representation is through pictogram.

[00:16:36]Now pictogram is a very interesting and very simplest I should say the form of visual and data representation.

[00:16:43]Okay. So here the pictures are being sent in the form of icons or symbols to represent the data and they're arranged in a single line or a grid and each line represents some kind of a unit. It could be usually 1, 10, 1, 10 or 100 and they are also known as pictograph, icon charts, picture charts and picture unit chart. Okay. So basically what it is doing pictogram if you look at it the whole purpose of pictogram is that it wants to make the uh data visualization more memorable it helps in the retention. So and it is best for visual memory and the purpose behind pictogram is that any boring facts any boring data can become very compelling very appealing as well and let me tell you another fascinating fact about pictogram it's not that pictogram has been introduced like just few years from now you know like with the with the advent of science but if you look at long long ago when uh the whole information in the early times had to be recorded so thousands and thousands of years ago I should Say even in the civilization of Egyptian or Sumerians we did find pictures that were you know basically engraved from the walls of the cave heroglyphics right and those simple base scriptures were able to communicate the information anything any record event any trade record even to tell the stories they use that kind of a pictogram but pictogram it gained you can say popularity somewhere around um 1964 when the Tokyo Olympics were organized. That was the first time that they started using pictogram, you know, in a public sphere with they started using a visual language instead of words. So now pictogram is used what um you must have seen at the fire exits, no smoking signs for transportation, any place you're traveling, the restroom, um baggage claim, departure gate and things like that. even in the public spaces the recycling the quiet zone and the um dis the the disabled washrooms or let's say you can say washroom for um physically challenged people right so all that symbols and through symbols they're basically telling us that yes that this is a this is a form of a pictogram now rules for drawing a graphical representation there are certain rules that you have to follow first select the right graph type you have to always match the graph with the nature of your data. So you use bar graph or pie chart for categorial data like gender, occupation and subject. And if you're using line graphs or histograms, you're supposed to use the continuous data.

[00:19:25]Okay, here like height, rainfall and temperature. Then you have to provide a clear title. Title tells you exactly what the data represents. So graph one just instead of writing just graph one or figure one you have to tell this is the average rainfall in Delhi and the time span from 2015 to 2020.

[00:19:46]Then of course labeling axis with units that's important. Remember in your school times when you did not write your the the units and how your marks were deducted because of that. So it's very important. If you've been writing that yaxis y x x-axis in years yaxis of rainfall which is in millimeters. Okay.

[00:20:05]So this is important that you have to write in the unit as well. Then choose an appropriate scale. This is very important. How are you representing your data in on the class interval. So if for example if the students range is from 20 to uh 95. So you select uh setting the um y-axis from 0 to 100. It makes a comparison realistic. But the more minutely you try to uh narrow your scale down. So it even the slightest different will appear too large.

[00:20:35]So this is important the what kind how the the the scale that you're selecting that should be also appropriate. Then ensure neatness and readability that means it the whole data should be very clean with very neatly drawn so can it can be easily represented and of course legend should be there. Now what is a legend? So legend in a graph is a key which identifies what are the different data series that is being presented here with different colors or patterns or symbols. Now see if you look at the data here uh you know that these are the avenues by in produced in different regions but like central mid-Atlantic and so on. But what is this red what is this blue? You have to represent you have to give that data here also. So this is where the legend will come. That means blue is books. Um red is electronics, movies and music. So legend should be very clear. Then acknowledge the data source. Source is very important. Even for example this I have produced this figure for your understanding. Right? So but here I also mentioned the source where I got the figure from. So even when you're presenting or you're writing an assignment presenting a data source is important that once you present pie chart or bar graph write the source that it you took this data from the ministry of uh education or the government of India and mentioned the year as well in which the data had been published.

[00:22:01]Now what are the general rules for graphical data? Now we look into it.

[00:22:07]First is the dose. What are you supposed to do? So like I said use appropriate graph type okay according to the data set that you have and then maintain clarity and simplicity use proper scales equal intervals starting from zero if possible right label axis we just have seen that titles legends units everything should be very accurate and you have to ensure accuracy proportion in the pie chart as well the bar length must be very correct okay now what are the tones that you have to be particular about when you're presenting a data.

[00:22:44]Don't overload the data with too much information. You don't want that. It beats the purpose, right? And don't use misleading scales as well. So, uh here I would say misleading in the sense that you you're showing that um for example like just like I said if you're using um too narrow uh class interval. So even a slightest difference would seem that the you know that the difference is very large the sales have doubled but in fact they have not but the kind of scale that you've selected that is giving the misleading information and don't mix inconsistent data as well right so the the the kind of data that you want to present it should be in continuation with the information that you want to show. So don't use percentage along with absolute numbers and so on. Then coming to know don't leave graphs without labels and legends right so you should tell like uh if it's a literacy rate uh rates of male and female that should be very clearly labeled right don't distort by using 3D effects unnecessarily because what happens is that on because if you use the 3D effect one slice of uh the pie chart for example appears simply big because of the viewing angle in which that you have portrayed the 3D effect which can also mislead the audience about its proportion. So be careful regarding that.

[00:24:09]Now let's look at the general principle of graphical presentation. So in the general uh you know the bar graph that uh bar graph papers that you have attached to your files and everything which is basically having these cells.

[00:24:22]So they are they help us you know to plot the graph accurately. So whenever there's a graphical representation there is always two reference line the coordinate axis right the horizontal which is known as the x-axis here this is the x-axis and the vertical that is the y-axis this is the x-axis and this is the yaxis right so of course and when we start the axis intercept at a point this is the intersecting point so all the values of the xaxis ES which are to the right of the origin that means here they will be positive and here to the left of the origin would be negative and for the y axis the values above would be positive and values below the um the intersection point would be negative and that actually the intersection of these two lines the intersection of two line divides it into four quadrants. You have quadrant 1 2 3 and four. So if you have uh any data that you want to plot for example if you want to plot two and three right points 2 and three so of course 2 is here and this is three. So both are positive.

[00:25:40]So it will be in quadrant 1. If it is -2 and minus3, minus2 here and minus3 here.

[00:25:48]So this is where we find that this is in the uh third quadrant. This is the point right here.

[00:25:57]So similarly any information that you want to plot here all you have to do is just trace the line first from the x then from the y see where does it intersect. If it is for example if I tell 4 and minus4 or 4 and -3 right 4 and minus3 so what do you do from four you trace a line -3 is here and this is the point right so be it is lying in the fourth quadrant. So this way you'll be able to plot and represent and you'll be following the general principle of graphical representation. Use a graph paper initially and once you have the hands-on experience then of course you can use use any kind of paper if you know how to you know equally justify the the axis and the information present on the both the axis. Okay.

[00:26:52]So this is all so if and all about today's uh graphical representation. So to conclude um you must have had a clear understanding of the objective types and what are the guiding principles of graphical representation which is enabling effective communication of data. So you see by selecting appropriate graph type and you following some essential rules so information can really become visually very appealing very accurate and easy to interpret and we need that we need all these qualities. Why? because we want to make our uh the analysis meaningful and reach a proper decision regarding the graphical representation. Right? So with this I've completed today's lecture on graphical uh representation and next lecture will be hands-on experience. So be prepared. We're going to work together and we're going to prepare different beautiful appealing graphs that we have just uh seen today and we'll have hands-on experience regarding that. So these are the different references that you can go through for any comprehensive um uh reading that you want to have about the statistics and the graphical representation. So thank you so much for your patience listening.

[00:28:05]I hope you had a nice time and I'll be seeing you again in my next lecture.

[00:28:10]Till then take care of yourself.

[00:28:11]Bye-bye.

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