all right so um the next graphical representation for quantitative data that we look at is the stem and Le plot also called stem plots okay all right so in this uh we have to split data values into stems and leaves okay all right let's use an example and walk through all of this all right so this example says that use the data set which will be walk away above for numeric gra of 20 um Georgia sou University students to draw a stem plot use the first digit as the stem and the second digit as the leave good okay so generally uh before you make a stem leave plun okay you will have to split your data values into two parts okay good all right so take from for example let me try to clean this out okay good okay so as of first step if you're trying to do a stem on leavea plot or stem plot okay then your um your first step so your step number one is to split your data values into a step and a leave good take for example maybe if your data set is 23 then um usually the uh left the rightmost digit the uh last digit is of your leaf and whatever you left with is your stem okay good now let's say that um you had a 23 say okay good then this part becomes your leaf and whatever you left with will be your stem good now let's say that you have a 12.3 then breaking this out this part becomes your leaf and what you left with is your stem good all right so um that is often the first step to make a step Lea blot and then we are going to uh arrange all the leaves horizontally corresponding to the same stem okay all right so let's use that example that we've seen in the slides to uh make a stem and leaf blot okay all right so let's say that we want to make a stem analytic blot for this particular data set so we want to make um a stem and oops stem and leave or temp plan for this data set okay as an A okay all right so as a first step we are going to break the data set into two parts if you use a vertical line on the left side you're going to write down all your distinct stems and you will write the leaves on the right side and you stu them horizontally so you want to go through this in an orderly man okay so maybe you want to go rowwise or you want to go column wise so I'm looking through all right if I'm going um uh if I'm going rowwise here I see an 0 good all right so that will be broken down into two parts all right so that is an eight on this side and that a zero so um you may want to go first of all um go through and pick down all the distinct stems so you have only two digits the left should be your stem and the right should be your list so I see an 80 something 90 something 70 something as I go on the first row the second row I see exactly the same things 80 something 90 something 70 something so my my stems are all going to be eight and then I have a nine and seven good all right so so again I go through from the uh left to the right rowwise so I see an 80 I know the Le will be zero I see a 91 the Lea is going to be one I see a 93 so that's three I see an 89 so that's N9 I see a 73 that is three I see an 86 that's 6 79 that's 9 77 okay I oops I see an uh I see a 98 so that gives me an a right here I see a 90 that gives me zero I see an uh 84 87 88 92 93 uh see 71 71 84 97 and 83 good okay so that is basically the uh First Step okay now um I want you to note that you must write them all um all the columns have to be the first columns have to be in line Second columns in line and so on and uh the rows also have to be all in line okay so you can get a better better picture of that data set good all right so as a second step step number two we are now going to arrange all of this all right so you arrange your stems from the smallest 7 8 n and you're going to arrange your leaves also from the smallest to the largest so let's go on with seven so you have one one three um s and nine now as you go 1 to8 what do you have you have a zero you have a three you have a four you have a four you have a all right so you have a four you have a six you have a seven you have an eight you have a nine good all right so if you go on to uh nine you have a zero you have one you have two you have three you have three you have um uh you have seven and you have eight good all right so what you have is called a stem and leaf plot that okay good now there are several deductions that you can make out of this all right so let's try to create our space out here to do some deductions that you can make out of this good all right so let's look at some of the uh deductions that we can get out out of this deductions okay uh now your stemma LIF plot can show you exactly where the center Li so if you basically Now flip this if you basically flip this vertically then you're going to be having something that looks like this maybe over here this is a seven8 and nine and then you have numbers that go all the way up to nine and then for eight it goes all the way to to 9 and then you have it for um nine going up to eight good so if you are looking at this picture you might guess though it's not too clear but you might guess that probably you're having something that is maybe uh close to symmetry but probably um probably skewed in some direction good right and you can also tell so this is maybe for the shape you can tell exactly where the center should lie you can also tell that you have low variability why is that because you have no GS okay good so those are uh things that you can deduce out of a um a histogram oh wait a minute out of a stem Le plot like this one now um the textbook provides all kinds of other techniques uh for example they talk about uh the splitting stem [Music] splitting stem uh splitting techniques and so on which can help you to have a better picture of your data set is that okay good all right so um that is the stem plot let's look at dot plots all right so um a Dot Plot is another graphical representation for quantitative data and just like uh stem and leaf plots okay uh do plots will be useful in cases where you have a small data set now let me say that if you have a huge data set stem and leave plots and Dot plots would not be very helpful in giving you um give you a clear description of your data set okay so you want to use a histogram in the case where you have a very huge uh data set or some other graphical representation okay good all right so um a dotplot which is again very useful when your data set is very small um is just a graph of dots okay let's use this example over here to make a Dot Plot draw a Dot Plot for the following data set okay good let me copy that over okay all right so let's see how we make a do plug for this D set okay good all right so um basically to make a Dot Plot what you need to do is just make a horizontal line okay let me try to put one over here to make a horizontal axis okay and you are going to scale that axis with all the numbers which you have from the smallest to the largest okay good all right so I have the numbers from 0 to 9 so that will be zero one two three four five six s eight n9ine good all right so if I have to uh that then that will be 0 1 2 3 4 5 6 7 8 and N9 good okay now um when whenever I see a number and I read it out I will have to strike it out and I write down and I I represent that number with the dots is that okay okay so um I can see that I have zero over here that appears three times so I will write for the dot three times one appears four times one good I see uh two three times one two three three so um they all have to be in in a line horizontally as well as in a line vertically okay there's no three but there's a five that appears four times so I do one two three four good all right now I see a nine that appears three times so one two and three good oops right oh boy okay good okay so um what you have where um this is you can always you note always don't tell your data this is called a DOT blot okay good and again there's several deductions that you can make out of this all right maybe you would guess um that you have in this data set there is a center now when we go on you will see that there's a center here there's a center here those are all centers measures of centers okay um several deductions you can um you can also see that you have a high variability probility why is that because you have a lot of gaps and again you may want to deduce that you have some kind of buy model set I don't know how that will behave but maybe this can describe some kind of shape to you okay good so there are several things you can ruce out of uh a DOT block especially when you have a small data set now keep in mind this is useful for small data set good you don't want to make a do plot when you have a large data set good all right so that's a do PL okay now the next graphical representation for quantitative data that we look at is a scatter plot all right so a scatter plot is useful when we have paired data in other words you have data data set that is made up of coordinates all right so let's look at an example over here so what I'm saying is that um for SC plot it's scatter plot becomes useful when you have a data set for example a pair data let's say maybe this is zero that's one and here is1 and this is two and maybe this is three and here is zero good okay now um the type of data which you make the Ty of graph which you make on your x and y coordinate axis okay generally that kind of graph is called a scatter plot if you do not connect the points take for example if I'm going to make one for this data set which I have over here I want to do my x axis and I want to do my Y axis good okay now um first of all uh we should note that uh we call our X over here is oops one second our X over here the x that we have generally is called your independent variable or the also called your explanatory variable okay good and your Y is your dependent variable okay good or also called your response variable now when we get to chapter five and four we are going to see this again okay good all right so for now if you're going to make a scatter plot for this data set what would you do okay so um generally your x axis that is where you have your X and you also have your y good now your X values go from 0 to minus one so that's 0o 1 2 3 and here you have minus one good while you have your values for your y going 0 1 2 good okay now um you we simply grab this points okay now when X is zero Y is 1 X is0 Y is 1 this is where you at when X is min -1 Y is 2 this is where you at and when X is three Y is zero this is where you at good all right so this graph basically is called a scatter plot without connecting any specific points is that okay good all right so let's look at the example that we have um in the slides and see how we make a scut plot for that problem good okay so we are asked to make a SC plot for this particular data set you're told make a c plot for the following data set representing the grades and number of study hours per week for five students okay all right so let's see how we make one good okay um if this is the data set that you have your first step is to determine your independent and dependent variables so your X which is your independent variable now which of these do you think depends on the order do you think that the numberal study hours that students make a week depends on the grades or the grades of in a course depend on the number of study hours the student make a we now um I would expect you to say that um your grades should depend on the study hours so your Y which is your dependent or response variable this should be what the gr and your X variable should be your study hours good all right so having decided that oops having decided that the next step basically for you is to make your axis and then you can uh you can now graph this okay so if you look at that say this is your y axis and here you have your x axis good all right so we know that on the y axis you're going to have the grds final GDs while on the y axis you going to be having what is that you're going to be having study hours good okay all right so the grd start on from six 60 going up to 90 okay good all right so let's try to do that so if you go one this is 60 65 70 75 80 85 and 90 okay good and your study hours go from 5 to 10 good so we can just do it from 1 2 3 4 5 6 7 8 9 10 good that's one 2 3 4 five 6 7 8 9 and then 10 good okay now um we are going to grab these points and what we want to do is where the two me we represent that point good so 60 goes with five a student studied for 5 hours on made a grade of 60 another student studied for 8 hours and made a grade of 80 right here another student started for um 10 hours and made a CI oops that's not okay good Med 75 so that is somewhere right here good another student studied for 5 hours and made a grade of 90 so that goes up again right here 0 another student started for um 9 hours and migr of 85 so that should go somewhere right here good okay so what you have without connecting any of these points is called is cut a plot okay good so what we are saying here is that what we have over here is called a scut plot good all right and there are so many things we can deduce out of this for example you can maybe guess that if you are looking for a relationship to represent the points you might probably have a straight line going on to the points maybe like this and that will mean that you are having in this case you're having a kind of of um negative slope oops you're have a kind of negative slope okay which means that as the points on the x- axis are increasing the number of stud hours increase maybe the students are not doing as good um practically that shouldn't be right because the students study more their grades should be high unless they're not doing effective study okay good so um those are the kind of things that you can deduce and we're going to see this more into um we have a name that we will call when we have a negative slope we're going to say that we have um negative arate correlation in this case okay good and we're going to do also specify the linear relationship linear relationship I'll Abate that linear relationship good okay so this is a scat plot okay okay the final um graphical representation for quantitative data that we make is uh a Time series graph or also called a line graph okay so basically we make a Time series graph or line graph when we collect data over time okay maybe um if you are trying to you're on a diet plan to lose weight and you have to take your weight over time maybe in months or weeks or daily um yeah you can always make a Time series graph for that kind of data set good all right so let's use this example over here to see exactly how we make a Time series graph all right so we are told that the weight loss of a GSU student over a oneyear period is shown below draw a Time series graph for the data set all right so let me copy this over to a writing space okay so if this is a data set which you have again A Time series graph has um a vertical axis okay and uh horizontal axis good all right now the vertical axis will always carry whatever characteristic you measuring over time in this case that is your weight loss and that is in pounds while the uh horizontal axis is going to be measuring um oh that is time good time all right let's try to wipe this oops okay all right um so this is going to represent time on the horizontal very good okay so um looking at this we have time in months going on from one up to 12 so I starting from some particular month and then go around up to the 12th month okay good all right so let's try to uh scale that axis right here so that's a one two 3 4 5 6 7 8 9 10 11 and 12 good all right so um writing it down that's one two 3 3 four 5 6 7 8 9 10 11 and 12 very good okay now um the uh weight loss goes all the way from 0 to six so we start here zero 1 2 3 4 five 6 1 2 3 four five and six oops six very good okay all right so we are going to grab the points okay and um we wherever we have um uh what corresponding time and weight okay we where the two meet we Mark the point we gra the points basically all right so in the first month the person lost three pounds okay so that was in the first Mon and that's three pound right here and the second month that was 5 pound in the third month person just one all right in the fourth that was two right here in the uh fifth that was zero in the sixth three [Music] and the seventh that is two right seven is two right here and the E month that was four and the nth zero 10 that's one um in the 11th one and in the 12th you have uh six right here good okay now what we're going to do next is connect each of these points with a line segment okay good so consecutive points consecutive points consecutive points consecutive points good all right so what you have here is called a Time series graph all right so this is called a Time series graph or you can also call it a line graph good all right so uh with this you do not connect to zero and you do not bring it down to the horizontal axis okay good all right so there are several deductions that you can make out of this diagram okay for example you can be able to identify different periods within the year where uh maybe the person had uh some issues going on this is a weight loss Pro um program so the person started pretty well as you can see um obviously doing well up to this point and then dropped a little so the person probably wasn't doing very well right here not very well right here here and then made some uh a little progress again and then dropped really wasn't doing well right here good okay so um you know things like this often can happen and you would not be able to identify them without a graphical representation like this maybe right here the person was sick or going through some stressful experiencing I wasn't able to keep up with the dieting or weight loss program and maybe right here maybe this is a festive period maybe Thanksgiving if that plan started in January and all of that so um you can always uh use a line graph like this to um visualize changes that occur over time um for a particular Curr reasing okay all right so that uh brings us to the end of this uh chapter and your test on um your test is going to be based up to this point and the corresponding homework okay all right so here is a little exercise for you and those are similar questions that can be in a test sample questions that can be in a test which of the following graphs can be used for quantitative data so instead of asking you that I can simply ask you a question like um um which of the following graphs can be used to represent numeric grades used to represent later grades stuff like that okay so you should be able to um identify the type of data and the different types of graphs that can be used okay all right