in this section i will discuss more graphs and displays so we're going to concentrate on using stem and leaf plots and dot plots as well as pie charts and pareto charts scatter plots and time series plots we'll discuss in a different chapter so but i want to concentrate on these graphs here so a stem and leaf plot is where each number is separated into a stem and a leaf and it looks similar to a histogram it still contains your original data values and provides an easy way to sort your data so let's look at this small data set and we can divide this up into a stem and leaf so the stem in this case would be two for the 26 and the leaf will be six so as you can see i have a picture of a little stem leaf you got the stem over here on the left the leaf over to the right and you can do this for each data value you can split it up into a stem and a leaf so if you look at the we got 21 we split that up the two comes first we put the one after it we got two 25s as you can see the two comes first and the leaf sorry in the stem and you got two fives as leaves then you got 26 27 28 you usually write the leaves in numerical order okay the next one we get 30 36 36 so your stem will be three and the zero six six would be the leaves and you only have 45 so your four would be the stem and the five would be the leaf so if we're going to look at a larger data set and it says the data set lists the number of text messages sent in one day by 50 cell phone users we're going to put this data in a stem and leaf plot so i'm just going to briefly explain to you again how to split it up but we had technology actually do a stem and leaf plot so as you can see the largest number here is 149 and the smallest number is 16. once again you use the right most digits as the leaf and the first digit as your you can either use the first digit depending on the number if it's three numbers you use the first two digit as the stem that's the leaf i'm sorry okay so we're going to list the stems right here we get it goes from one all the way up to 14 and then the leaves come after it you really have to pay attention to the key as you can see the key has 10 with the slash and then two that means 102 but sometimes this key can be different this could actually mean 10.2 okay so always make sure you understand what the key is telling you uh what the stem and leaf represent so as you can see it you got all your data values in this in this stimulate plot if you look here this one six is one slash six means sixteen okay this one slash nine means nineteen and it keeps going also if you look here the 13 does not have a value even though you the 13 means 130 131 132 all the way on but we have no no data values within this range from 130 to 139 so we still write the 13 but we do not put a we do not put a a leaf after it we just leave it blank a lot of people forget to put the 13 there because they think that oh okay well since you don't have any numbers within this range we don't use these first two numbers but if you do that then your graph will have like gaps in it and that's not what you want it won't be consistent so you have to put the 13 there you just do not uh put a number after it so the reason why we say this looks like a a histogram is if you tilt your head to the side you can see a pattern so if i do it if you like draw not really good at drawing sideways but if you tilt your head you can see a histogram okay and you can see that more than 50 of cell phone users sent between 20 and 50 text messages okay just by looking at that so that's one way to display data typically um when you go out into the real world you don't use stem and leaf plots okay so like if you ever reason read a newspaper article or some type of statistical journal you you'll likely never see a stem and leaflet but this is a good plot to use if you have a small data set and you you just want to see a pattern real quickly you can use the stem and leaf plot another plot that we have is a dot plot once again we usually don't see dot plots out in the real world but to do a dot plot you take each data entry and you plot it above a horizontal axis so once again we have this small data set my horizontal axis goes from 20 to 45 and then we just plot each point above its corresponding number so you got 21 we'll put a dot at 21. we got 225 so we stack the dots on top of each other the same thing for 36 you have 236. so let's go back to our previous example with the text messages and we're going to put this into a dot plot and this will we we can use data for dot plot statcrunch would do a dot plot um excel will not but this is how your data set will look and as you can see um it looks like most entries fall between 20 and 80. so maybe most most of your data values fall within here um as you can see this 145 is far away from the data you would consider that an outlier or an unusual data value so maybe this person just text all day long who knows but it looks like the majority of people send between 20 and 80 text messages now one graph that you'll see out when you go into the real world is a pie chart and it provides a convenient way to present qualitative data graphically as per sense of a whole a circle is divided into sectors that represent categories and the area of each sector is proportional to the frequency of each category so once again pi chart is used with qualitative data so we or we can also say categorical data your data values are in categories so the numbers the numbers of earned degrees conferred in thousands and 2014 are shown in this table we're going to use a pie chart to organize the data so as you can see we have an associates we have one hundred three thousand bachelors one thousand eight hundred seventy these are all in thousands masters seven hundred and fifty four thousands doctoral one one hundred seventy eight thousand that 103 thousands that's like a million okay that one eight seven zero thousands is a million okay that's over a million one million eight hundred seventy thousand is what that means but it's just truncated so in order to construct a pie chart we're going to use the central angle that corresponds to each category to find the central angle you're going to multiply 360 degrees by the categories frequency so if we go to the first one we have the associates the relative frequency was 0.264 remember we calculated relative frequency to be the frequency divided by the total number of data values in this case we have three thousand eight hundred five when we divide that out we get point two six four we're going to multiply that by 360 and that gives me a 95 degree angle but remember circle is 360 degrees so 95 is just a slice of that 360. when you do a pie chart you usually put the relative frequencies or you change it to percents on the graph so this point two six four would be twenty six point four percent of people had associates okay and the reason why i we use percentages is because um if you look at this table you know you just have numbers you don't know what proportion of all the degrees are that a bachelor how many people earned a bachelor's we don't know that proportion just by looking at the number like we said 754 thousand earned a master's okay well what percentage is that of all all the degrees earned so rather than just looking at numbers we want to look at the relative frequencies so you can do um pie charts in excel and statcrunch so i've already set this up in statcrunch for you it's over here to the left i have the associates bachelor's master's in doctoral and then the frequency so to graph this we're going to go to graph pie chart and we're going to do with summary this data is already summarized in the table so when i click on it i want categories the categories are located in the type of degree and the counts are located in the frequency column right next to it okay i have two frequencies on here but just ignore that second one because that's for a different problem and then i want to do percent of total this is going to give the percents for each one of my slices and then i'm going to hit compute and i get this beautiful graph now the percents are actually on the graph is over here on the right in this ledger so it tells me that 26.36 26.36 percent got an associates and that's in the blue color so it gives me each one and this looks just like the one i have on my pie chart you can also do this in excel i already have the degrees and frequencies already set up and remember if you get a problem like this in your homework you can send it over to statcrunch or you can send the data over to excel so in this case i got everything set up i am going to go to insert and you'll see this little pie right here it says pie chart but before i do that i need to highlight this so i'm going to highlight the first cell i'm going to click on it and i'm going to hit shift and then i'm going to highlight the rest of the cells that contain the data so i go to insert pie and i click on it and i get my pie chart now as you can see we don't have any uh any numbers on this pie chart but what you can do is uh click on let's see click on this plus sign let's see if that's the one i want maybe i should click on this one okay now click on this little paint brush if you click on the paint brush you'll see different types of styles come up you can scroll through and i want the one that contains percentages so i want this one right here and once you click on that the percentages will pop up on the chart your ledger is all in color so the blue is the associates is 26 percent the master's in gray and that's 20 percent and the doc the bachelor's is 49 that's the orange another way you can display data is in the pareto chart and it's like a vertical bar graph in which the height of each bar represents frequency of relative frequencies in a pareto chart the bars go from go in order from decreasing height so it goes from the largest the tallest down to the shortest okay the tallest is to the left the shortest is to the right so a bar chart deals with categorical data so let's look at this example here in 2014 these were the leading causes of death in the united states we had accidents 136 053 cancer 591 699 all the way down to a stroke 133 000 103. so we have five uh categories here and we're going to use the pareto chart to organize the data okay so when you organize the data like i said you have to put it from the largest amount down to the smallest and it goes in decreasing order so we can also do this in statcrunch i already have this data set up in statcrunch is over here to the right and you go to bar sorry graph by bar plot bar plot with summary the categories are the causes of depth and the frequency will be the one next to it and when it says order by we want to order by account descending and when i hit compute i get my chart and as you can see heart disease is the leading cause of death all the way down to stroke the bars go from tallest to shortest you can also do this in excel i already have my data values in there we're going to go to insert and we are going to go to this histogram and we're going to click on it and if you look at to the right of it it says a pareto chart okay so i'm going to highlight the data first go to insert and then click on the pareto chart and there you go and it gives you your categories along the horizontal axis as well as the frequency along the vertical axis you have this line here this orange line you can ignore that it does have depending on what type of statistics you study we can discuss this line but it's not discussed in this course and this is basically this is a cumulative graph that's what this thing is it's an ogive and we talked about ogi before but with excel it gives you an ogive chart it doesn't give that to you in statcrunch okay and as you can see both of my charts look like uh the ones that is on my powerpoint okay that's the end of the slide