 Welcome to session 5 of Quality Control and Improvement Using Minitab. So, I am Professor Indrajit Mukherjee from Shell HMF School of Management IIT Bombay. So, we are discussing on tools that are used for visualization ok. So, in this context we are just discussing about histogram where it can be used and what scenarios like that. Histograms are generally used whenever I have a continuous data. So, for that generally histograms are preferred. So, there are many key quality tools which we will highlight over here. So, one of the tool is histogram another one is box plot that is the two important tools that is used in quality. So, visualization of the data. So, and that can be used for some interpretation out of the data. So, that we will see how it is possible. So, here you see I will talk about box plot over here I will talk about histogram and then we may go to scatter plot over here. So, histogram is just representation of the data. So, how the data is spread over here. So, what is the spread of the data that can be seen. So, there can be a spread from this range to this range like that and where is the peak of the data concentration of the data CG of the data basically CG of the data may be somewhere over here. So, but the spread of the data is showing that there are two clusters over here. So, one is this cluster over here and one cluster is over here. So, that means, a mix of data is basically plotted over here. So, it will give you some sense about the data distribution like that and what is the spread of the data. Then we can see the descriptive statistics in Mineta which can be used to see what is the mean value, what is the other measures or statistic that can be that we can we can also figure out that means what is the mean, what is the standard deviation like that and what is the range, what is the maximum, minimum, interpreted range all things are possible over here. So, let us take an example of CTQ and let us try to demonstrate that one. Let us try to see that assume that CTQ is thickness like that. So, we will illustrate in Mineta how these plots are possible. So, last time also we are discussing on this. So, I will open some data sets which is available with us and that will help us to illustrate in Mineta like that. So, I am opening in Excel. So, some other data sets and then we will place it in Mineta like that and see. So, there is a layer thickness which is an important characteristics which we want to plot over here which is a CTQ basically. There are marks in quality also we can illustrate. First let us try to see that in a manufacturing process some we are producing some thicknesses or coating over a given surface. So, in that case layer thickness is important and target value we can assume as 3. So, let us try to see by plotting this one whether some more information we can get out of histogram like that. So, I have copied this data set over here. So, I told you that when you install Mineta what will happen is that a icon will be coming to your desktop like that and then when you click that icon what will happen is that we will get some interface like this. And we can we can just see the interface over here and see once these are the columns where you have to cut paste the data set. So, first row over here where you can write the data name of the data variables like this and then you can type in the data also or you can copy paste the data from excel sheets like that. So, I will copy paste the data from over here and I have already copied this one and then what I will do is that in Mineta this worksheet what I will do is that I will highlight on the first row and then I will control V I will paste this one ok. Whenever I pasted this one so there are there are windows over here. So, what do you see over here this is the session window where the results will come when you do some analysis over here and if you have to save this worksheet which is coming over here. So, this worksheet this is known as worksheet over here like excel what you see worksheets like that. So, this can be saved over here save worksheet as. So, what you can do is that save worksheet as and then on the desktop maybe we can we can save this one. Let us say visualization of data I am going to replace this file which is existing like that. So, I am just replacing with a new file like that. So, you can you can also name a new file like that because I had already created earlier. So, for some illustration. So, again I am redoing that one I have replaced that file. So, now this file consists of only c 1 columns with layer thickness like that ok. Then I told that where from I will draw the graph. So, there is graph option over here there are many options that you can see over here. So, out of the all the options you have histogram over here as one of the options like that. So, there can be other options like that. So, I am considering on histogram over here. So, for visualization of the data this is a continuous data continuous scale data. So, that you can understand thickness is measured over here and it is a least count is up to 3 decimal place which was measured over here ok. So, what I will do is that I will plot this histogram over here. So, I clicked histogram. So, then it will ask simple histogram like that ok I will mention it ok I will draw a simple histogram like that. Then what is the graph variable your cursor should be over here and double click this c 1 column over here or otherwise what you can do is that I can just delete this one I can just highlight this one and select from here. So, that is also possible. Then you have some scales over here keep it as default do not want to change this one labels I do not want to if you want to name or give some titles that you can give ABC or something like that this is always possible. So, I am not doing this this you can explore by yourself like that ok. So, data views and all these things do not do anything over here we do not want multiple graphs to be plotted. So, data options are over here. So, these are also not required because I have already given the options that layer thickness has to be plotted ok. So, maybe the frequency over here which you want to which you want to highlight over here. So, maybe that if that information is available. So, in this case that is that can be provided over here that is not required over here. So, label what we can do is that maybe data labels what we can do is that use y values to data label over here. So, in this case what will happen when I when I click ok over here I will get the frequency information also. So, this session window will give you this window will give you all the results over here and graphs. So, when you double click this graph you can you can just see that Minitab has already done the basic analysis and it has plotted the histogram based on the its default options that is there. So, number of classes what do you see over here 1, 2, 3, 4, 5, 6, 7, 8, 9 classes it has divided the total dataset and the width of the classes is the interval which Minitab automatically determines like that and there are formulas to do that also. So, in that case Minitab does it automatically for you and gives you the frequency. So, this over here what you can see this is the bin size over here. So, this is varying from 3.015 to 3.025 like that and within this bin there are 5 observations like that. Similarly, next bin you can see how many or in that class how many observations like that. So, maximum observations are within this range over here what you see 3.07. So, it is varying from this range over here. So, this is 3.055 and this will be around 3.075 like that. So, we can assume 3.07 more or less is the average or center of gravity or accuracy or what you can see the CG of the dataset like over here. So, and the spread of the data varies from this range to this range. So, what you can see that peaks of the dataset. So, we can also plot this one by we can also what we can do is that when I draw histogram it will ask width fits like that. So, some normal distribution overlay graphs can be placed over a distribution graph can also be placed over here. So, if you click ok. So, it shows you some normal distribution plot over here. So, mean is given standard deviation is given number of observation is 72 that will be given over here. So, this observations and also you can copy this graph like this. So, if you want to copy the graph and paste it in reports or in excel file like that you paste it over here and just move wherever you located. So, this is possible in board and this is also possible in excel like that. So, you can save these graphs also ok. So, that is also possible. So, this gives you some basic information. Now mean standard deviation I may need more information over here. So, that will not come in histogram over here. So, maybe maximum values, minimum values. So, then what I have to do is that I have to go to stat and they go to basic statistics and maybe display descriptive statistics like that. So, one go you can draw histograms also using this option like that. So, minute I have this stat option where we will use basic stat regression and over in this course is another experiment control chart quality tools. Some more with respect to time we can plot also which is known as time series we will not cover, but we will show you some illustration of graphical illustration how it is done. So, minute I have options of nonparametric test like that those are the test we will also illustrate in certain scenarios where it is required like that ok. So, what we will do is that now in this case. So, I want to see the basic statistics. So, in this case display descriptive statistics I will mention which is the. So, cursor will be here and double click c 1. So, what are the statistics that will be required? So, I have gone to statistics and I have clicked that one. I want mean information, I want standard deviation information, variance information, coefficient of variance information, first quartile median these are all informations what I want to see like that maximum minimum range these are not required. So, maybe these are the basic things one wants to see in the data set. So, in this case I will click ok and if you want to see histogram over here also with normal fits like that that is also possible like that. So, this when you click this one. So, this comes automatically like that in minute tab. So, now this things can also be the results can also be copied as a picture like that and you can just place it wherever it is required. So, if you want to place it over here you just place it over here and then save that one or in reports anywhere ok. So, what information we get over here mean value is 3.060613 like that. So, up to fourth place of decimal data sets we are getting standard deviation coefficient of variation that means what is the magnitude of variance with respect to mean like that. So, variance information is also given over here minimum maximum inter quartile 1 quartile 3 median value that 50 percent observation are less than this 50 above this one like that. So, range information is also given inter quartile range is also given like that. So, all informations we can get out of the minute tab software which is necessary over here. So, mean is 3.06, but I told you initially that our target is 3 that means CTQ that is generated thickness layer that is generated over here should lie between 2.9 to 3.1 let us say and the target value is 3. So, what we can see from this graph is we are basically off centered like that you see. So, 3 is around on this axis on the left hand side like that and our average what is coming out of the process is around 3.07. So, we are accuracy part we are missing over here and also we are getting some information which is beyond 3.1 that is out of spec also data we are generating over here ok. So, that is also an alarming situation in quality that means our process is off centered variability is high and also we are producing which is creating rejections also. So, this gives you an immediate impression of the data set without much statistics I can make this kind of interpretation out of the data ok. So, another important thing what can be done like that when whenever I have the spread of the data we can also see another important graphical illustration over here which is known as box plot like that. So, here also box plot is sometimes used to define some of the. So, this is what it will show is that what is the width means within which we have the complete data set like that. So, this is the range which is known as inter quartile range within which most of the data sets are concentrated over here. So, if it is more spread that means we have a much variability in the data if this spread is very less or we have a small spread of this. So, in that case data is squeezed more or less over here and in that case density of the data is high. So, variability is less we can also interpret like that way. So, it is like spring more it is spread more elast that means more data spread of the data is quite high and if this is less squeezed that means we have a much less variability in the data like that. So, we can think about that and these are the stretchable extension what you see over here. So, these are known as whisker over here. So, this line what you see over here extended up to 1.5 into inter quartile range what you see over here definition and anything lying outside this is basically outlier over here that is indicative measures that it takes like that. Anything beyond this is an outlier there are other tests for in identifying outliers, but this is in box plot also we can see that which data is very unusual like that. So, that we can we can also see from the box plot. So, this on this the first start of the box over here this is known as first quartile Q1 and this is the second quartile which is known as Q2 or the median value of the data set where 50 percent of the observation will be on the right hand side of this value and 50 percent on the left hand side left hand side of this value and right hand side of this and this is known as third quartile values over here and difference between this first quartile and third quartile this this area is known as inter quartile range like that ok. Here also whisker is extended to the smallest value 1.5 of that and anything beyond that is outlier basically ok. So, this is also possible in Minitab. So, we will use the same data sets to illustrate box plot where we have drawn histogram here we want to see the inter quartile and where the data is most concentrated like that. So, what we will do is that that is also possible over here. So, that is also possible over here. So, this same data set we are using. So, I will go to Minitab over here and then what we can do is that we can just see the box plot and then we go to graph and there is a box plot option over here. Then there is simple box plot over here I click ok and I give the variable as c1 double click that one and do not go I do not need to see much options over here. So, we can we can place the values over here also. So, just click on this and you will get all information. Quartile 1 is 3.04 that is 25 percent of the observation is less than this 3.06 is a median value. So, 50 percent of the observations are below this and 50 above this one. So, this is the inter quartile range like that. So, this is the spread of the data set what we can see. So, most of the data set are concentrated in this zone like that. So, data set concentration can be seen over here. So, this is the width of the box like that. So, most of the data are concentrated within this ok. So, this is the inter quartile range. So, this information we can get and how this is useful like that I will I will use an example to illustrate that one. So, let me also take some examples like that like let us say the quality marks and which I have not discussed or what we have started like that. So, I am taking this marks in quality I have to make a decision let us say whether to attend the course this is the last year marks what I have what was given. So, I want to select whether to go for this course or not like that. So, what we can do is that just we can see the basic statistics of this. So, display descriptive statistics I will display the marks like that and statistics what we have mentioned is already given over here. So, and graphical illustration I want to see the box plot of this rather than histogram. And so, I will click that one ok and I will click ok over here and then I will get the box plot over here. So, on an average the 50 percent median value is approximately equals to 72. So, that means, on an average people are getting what we can say is that the middle value 50 percent of the people are below this, but 50 percent are above 72 like that. So, this is a favorable situation what we can see over here and also we can see that 72 is the average value from here. This can also be copied like that results can also be copied from here copy as a picture like that and you can paste the results what I have shown earlier also over here. So, statistics can be pasted like that. So, that is also possible. So, in this case what we are seeing is that on an average 72 marks are there. So, I can also see the histogram of the data set and if you want to see the histogram of the data set then some more information we can get like that just click double click that variable graph variable and click ok over here. And then what you see is that you will get the histogram of the data. So, what you can see is that on the left hand side much less observations are there and on an average 70 is the we can say center of gravity of the data like that. So, most of the people are more than 70 what we can see over here. So, this is a favorable situation just by drawing what I am seeing is that number of people getting more than 70 is much higher as compared to the number of people getting less than 70 like that. So, so that is also reflected over here. So, it is more skewed on the right hand side as compared to the left hand side like that. So, on the higher side of marks basically. So, in this case I can make immediate judgment ok this course in that case I can take a chance because people are getting more than 70 most of the people are getting more than 70 is like that it is skewed on the right. So, that is why this is a favorable situation like that. So, that also is possible, but if I want to make a box plot interpretation also I can see that one and I can also see the marks information and I can draw the box plot like that and when I see that one also I see the same information, but there is some variability over here and but favorable is more than 70 many observations are more than 70. So, you do not see symmetry over here. So, more observations on the other side. So, density of that is more. So, color blue is on the. So, it is not symmetrically what you see like that. So, there is this more values on the other side. So, skewness will be represented also in box plot you can can directly see which side it is more skewed data is concentration. Data concentration is more on one side as compared to the other side like that. So, that gives you an immediate impression that what we what we can do out of this data that we are. So, some inference we can draw some decision we can make out of this. So, box plot can also be used we can draw multiple plots over here. So, let us take another example like I have some data set where rest went information is given and I want to see which restaurants to go which has minimum service time. So, some data is provided over here. So, like Burger King, Pizza Hut, McDonald's, Subways, Domino's Pizza and all are providing burgers let us say and I want to take wherever there is a least time like that. So, some random sample information is given over here. So, this information was collected by some researchers and based on that I have to make a decision which restaurants I should go like that. So, what I can do is that I can just copy this information I do not know much about statistics, but I want to place that one and I want to compare these data values like that. So, in this case in in one go I want to analyze this one. So, Burger King this data I have pasted from there copy pasted from excel and then I want to see that how it box plot can I see multiple graphs in one like that. So, what I will do is that I will go to box plot over here then I will go to multiple y options over here I click ok over here then then I what I do is that Burger King from here and I press shift and I select up to C 10 like that. So, then I select this one and it will automatically or otherwise what you can do is that just double click one then second one third one fourth one and fifth one like that and keep it as default and whatever conditions. So, you will get this graph in the session window like that. So, if you enlarge this graph what happens is that you can see in one scale in one graph you can see the variability of the data set like that. So, the Pisaert condition what you see is that this is the median value over here and the median value is coming out to 143 which is very which is less as compared to any of the median that you see that that central line that you see any of the median. So, this is the lowest it is giving you the lowest median that means you can you can also see that this information helps you that what is the median value of the observations which can be taken as a location of the data central tendency of the data set like that that also we can we can consider sometimes medians can be useful for that interpretation also, but mean also can be calculated we can see the values of means ok. But what it says is that the median value is very low is lower than any of these options. So, immediately I can discard Domino's Pisa because this is very high. And then subway it is also high and variability is also high this bandwidth of the box that you see over here the bandwidth is quite high. So, this is also not favorable for me and this is also quite high Burger King is also quite high. So, I have options between Pisaert and McDonald, but if you see Pisaert and McDonald what comes into my mind as bandwidth of the Pisaert that inter quartile range is quite low as compared to McDonald over here. So, I will I will select Pisaert because that is the service time of Pisaert is less as compared to McDonald over here. Although you can see some outliers over here there is some service disruption may have happened in one or two cases like that, but I may be willing to take the risk like that. But if it is on the lower side you see that one star is over here on the lower side of this this is also an outlier, but this is a favorable situation if you see delivery time less means it is a favorable situation. So, in this case I am not worried about this and these two I can I can take it because I can see that most of the observations are having less variability in service time. So, variation in service time is also less and the median value is also quite less. So, I will I will take a decision to go to Pisaert and take the deliveries like that. So, if I have to choose between any of these restaurants based on the data I will choose that one. So, a multiple box plot can be shown in single graph like that that is also possible in Minitab like that. So, that is a quick understanding of the data I will have visualization of the data that is possible in many situations we will have such kind of plots which will be helpful in quality also quality also like that. So, so this is box plot what we have illustrated. So, you can just practice that one and see some of the data sets of CTQ and plot in single one or plot in multiple plots in single graph like that. So, that is also possible like that. So, then we can what we can do is that we can also understand and plot like dependency between variables like that which is known as scatter plot. Sometimes what happens is that this is extensively used in regression like that. So, this can be used in regression and we have regression analysis like that. So, I will so this is one variable like that. So, this is one X variable on this axis over here. So, and the other axis is Y over here. So, this is another axis what we can see. So, here what is important is that whether there is any relationship between the data set or not. So, that I want to I want to check. So, whether there is any relationship that X is between the two data set like that X and Y like that. So, there I will see this is extensively used in when I am trying to develop a function between Y and X like that. So, so that is where we will use like that. So, if I am interested to illustrate that this is a X variable Y is a function of X I want to see that one and whether linear function nonlinear function. So, this scatter plot will help me to understand that whether one increases other also increases or not like that. So, what is the correlation that exists between the data set strong relationship or weak relationship like that linear nonlinear many things are possible over here ok. So, this will help in regression analysis and regression is an important tool in quality. So, that is used in design of experiments also ok and that is also used in prediction many of the times predictive models are used to control the process like that to get the best CTQs like that. So, that is also an important aspects what we cover in quality. So, that is but you can you can see any any regression analysis in many of the course like statistical course like that. So, we will give a brief idea of regression also in this course ok. So, what I wanted to illustrate at that this gives a demonstration between relationship between two variables. So, this is known as scatter plot and the relationship can be like this. So, you can see that x and y is on this axis. So, in this case the relationship between these two variables name you can you can you can change it. So, one axis may be x 1 other axis may be x 2, but x and y is the I am trying to trying to say that one is the CTQ and one is the control variable. So, in this case control level variable. So, that I want to illustrate over here and for that what I am doing is that I am showing. So, this is a linear relationship. So, what we can see is that one increases x increases on this side y also increases like this. So, here you can see some curvilinear relationship exists like that. So, this is x increases initially it increases and then it becomes steady and then it becomes down like that. So, it is a non-linear kind of scenario. This can also be thought of as non-linear relationship means this is a polynomial equation basically. So, maybe x square is prominent over here. So, in this case some square equation will be prominent over here and here it can be negative relationship that means one increases other goes down like that. So, one is decreasing. So, one is increasing this can be positive and this can be negative relationship what you see over here. So, these are the types of relationship when you plot that one you will immediately you can visualize that one and immediately you can make a interpretation out of that. So, visualization of the data set like that. So, then here you can see that if the density of the data are more concentrated towards this then that means a strong relationship. So, bandwidth of this is very less and all the data points are within this. So, this is a strong relationship positive one and when positive means when one increases other also increases like that and linear relationship that we have to take into mind to consider. So, but the width is very high over here. So, in this case not very strong relationship. So, how do we say strong weak like that? So, we have a correlation coefficient to understand the relationship between variables like that. Pearson correlation coefficient can be seen to see linear relationship between y and x like that if x increases y increases what is the strength of the relationship that can be seen like that linear relationship I am saying. So, in this case there are options like that. So, this can be seen like that. So, this is now there is no relationship you see random variable random ups and downs like that no trend as we can see increasing decreasing like that nothing is possible over here. So, and this relationship what we see over here can be expressed in mathematical terminologies like that which is known as correlation coefficient over here which is given by covariance a measure that association between two variables divided by standard deviation of x variables standard deviation of y variables. This is the covariance formulation over here what you see and covariance divided by these two will give you information about the strength of relationship. So, r lies between minus 1 and plus 1 like that. So, this will be the minus 1 plus 1 relationship that you will see like that ok. We will take an example to illustrate that one. So, let us take one examples to illustrate this one relationship between both variables how it can be done in Minitab. So, I will take one example over here and let us take a simple example scatter plot examples like that and where we have size of the flat and price of the flat and I want to see whether relationship exist or not. So, these are coded variables. So, I am just copy pasting the information. So, and I am pasting it over here. So, in this case I will paste the information over here and then what I will do is that I want to see the relationship and first I will draw the scatter plot and then figure out what is the correlation between these two data points like that. So, what I will do is that I will first option is scatter plot over here. So, when you when you click this one what will happen is that it will show do you want a simple scatter plot? Yes, I want a simple scatter plot there are many options with regression and all these things I am not interested I want to see. So, which is the y variable I am taking arbitrarily price as the y variable and size of the flat as x variable over here there are other options that is available over here I am not going into the options you can always explore that one I will click ok over here and it will give me a visible impact over here. So, if you see the graphical illustration that indicates that size of the flat increases price also increases like that. So, this gives you an impression that may be they are related may be they are related over here ok. So, and positively related over here linear linear relationship may exist, but the strength of the relationship I need to check. So, in this case strength of the relationship how do we see the strength of the relationship over here then I have an option to see that one. So, basic statistics then I have a correlation matrix the formulae that I have shown covariance divided by standard deviation of x and standard deviation of y that formulation what we have shown over here this formulation will be used like that. So, this is s x y by s x by x y. So, this is the relationship it will indicate what is the value of r. So, r is on the positive side plus one side. So, that is positive strong positive relationship on the negative side towards minus 1 and close to minus 1 strong negative relationship linear relationship basically ok. So, then what I can do is that I want to see this one. So, in this case Minitab I will use this one stat basic stat calculation will be done based on the data set x and y over here which I have defined. So, correlation between two variables. So, I want to see price and size let us say. So, you can you can just so sequence of this is not important whether price is placed first size is placed again it does not matter. So, option is that I want to see Pearson correlation over here. So, in this case and graphical matrix plot over here. So, what you want to see over here I want to see correlations between the variables like that. So, only there are many options so statistical interpretation. So, I will use the simplest one over here. So, I will click ok over here then what do you want to do you want to see the tables like that. So, whatever default also you can keep like that ok. So, correlation coefficient is coming out to be r 0.727 like that and so this is the correlation coefficient that you see over here. So, this is the Pearson correlation coefficient that you see over here ok. So, variance also what we can see is that basic stat we can also see the covariance of this we can calculate. So, in this case covariance of this will be given like when you do that one. So, this is the covariance matrix what you see over here. So, in this case so covariance what you can do is that price and size covariance is 191 basically. So, what I can do is that I can open a calculator also and I can just see the calculations whether it is rightly calculating whether Minitab is doing it correctly. So, 191 has to be divided by standard deviation. So, size and size this is 27 approximately this is 2545 like that. So, square root of these two values when you multiply and then make a inverse and then multiply with 191 you should get the correlation coefficient like that. So, I am making a square root of 27 let us say and when you do that one around 5 I can assume like that 2545 I will take a square root of that and it is about 50. So, 50 multiplied by 5, 250, 50 multiplied by I am doing 5 let us say and 250 and make a inverse of this and then multiply it with 191 that is the information that we have and what we get is 0.75 approximation over here. So, in this case and what we got earlier was a 0.75. So, earlier what we have got correlation coefficient. So, in this case what we have gone is that approximately 0.72. So, some calculation error is coming because of square root and all but it is perfect. So, 7 to 7 if we go by exact calculation method. So, it will be same the value will be 0.5 to 7. So, that is possible. So, that is possible. So, we will ignore the last part of this. So, we will consider that one. So, what is important over here strength of the relationship. So, this is 0.72 what we have seen over here what we have seen. So, graphically what we have seen and positive. So, 0.7 to 7 that is positive and generally more than 0.7 can be considered as a strong relationship and this is on the positive side because this is plus r equals to plus 0.7 to 7. So, that means I have a somewhat strength of the relationship is quite high linear relationship is quite high over here. So, that can be also seen over here. So, this type of analysis how it will help is that it will try to identify like that. So, when I am defining a variable between relationship between two variables over here. So, y is y and x over here and in that case whether they are related or not that will help me to select the x which will be used in design of experiments and experiment on those things to develop the functional relationship y and x like that. So, this can be one of the x that I am trying to see the scatter plot because there is a 2D plot like that and if you have more variables we can add more variables over here 3D up to 3D plots are possible that can be visualized basically more than three dimensions cannot be visualized. So, in that case and it gives you some common sense that this is a potential variable which can be considered when I am modeling that one y with x or which variable can be considered in experimentation to understand when I change the x it will have impact on y. So, we do not select arbitrarily we select those x and manipulate and try to enumerate those x at different levels and try to experiment on using statistical means ok. So, to understand the relationship between y and x like that. So, selection can be initial selection can be based on correlation information like that. So, with this illustration so, we have we will stop over here for this session. So, what we have done is that we have shown you histogram where the data can be plotted and CTQ and we can see the variance of the data and we can we can also see the central tendency of the data then with MINITAB and that is quite convenient like that. Then we have a box plot where the straight or the data like spring I can see that concentration of the data is more between these values and these values first first quadril and third quadril. Inter quadril range can also be we can think about the spread of the data like that ok. Box plot helps you like that it can be used for multiple scenario comparison. So, which is the best option like restaurants what we have taken. So, that is one important plot. So, in quality I am demonstrating three important plots in this session. So, one is histogram, one is box plot and the last one what we have demonstrated is relationship between variables because this will help me to select the X variables or control variables which impacts Y basically. So, whether there is any relationship between X and Y and I am showing linear relationship like that. So, non-linear relationship also can exist and in that case those variables can be selected for experimentation and finding out the mapping relationship between Y and X which can be used for optimization also. So, this is the overall idea and we will stop over here and see you in session 6 and where we will discuss more about quality visualization of data and which are preferably used in quality control and improvement like that. Thank you.