this is the list of data that you have on the top of page 20. I just had to write it in two lines because I couldn't fit it up here I just want to make sure I had it to point at it so there's some numbers there um maybe they are ages maybe a bunch of people at a family reunion that would make sense right but we have ages between the smallest one of six let's pick this one 70 yeah I mean that could be people at a family reunion between ages six and seventy a bunch of Ages so that's just a long list of numbers if I ask you some questions about it like what what's are there more younger people or older people is it evenly spread out from young people to old people is there any group that is more of or less I could ask you all these questions and it'd be a little hard to answer the way it's just written there in the list well let me start counting I mean the first thing you might want to do if I ask those questions might be to rearrange them uh that's what a stem plot does a stem plot is the first thing we're going to do it rearranges the data it puts them in order nicely and even tells you about the distribution maybe it's distributed normally we'll see that so we're going to make a stem plot there's two vertical lines on your paper the second one is actually going to be our stem plot the first one is what I call my scratch paper to get started with my stem box your stem plot takes numbers and breaks them into separate digits in this case these numbers all have one digit or two digits they have to all be the same either all B2 or ob1 for us to compare them but I'd argue that we could write for example nine as a two digit number if we wanted to what would it look like zero nine right so we could make this I mean we don't usually write it that way but if we had to make it a two-digit number we could kind of like if you're doing like the pennies part if you buy something right you put .09 right same idea so then we could write them all as two digit numbers if any of them were three digit numbers we'd have to write them all as three digit numbers so that would be zero zero nine okay so they have to all match and then we say okay once the we separate the last digit there's one digit at the end which means they all have one digit at the beginning just looking at the first digits what are my first digits what's the lowest first digit and the highest first digit in this list of the first digit S zero and sorry seven seven okay because I've got things from one digit numbers up to I think 70 is my highest so the first digits are going to come over here but they call it a stem plot this side they call the stems and this side they call the least leaves some people call the stem and leaf plot so my stems are the first digits zero one two three four five six seven it doesn't matter if I don't have one of each of these I have to have everything from the smallest to the biggest represented here so if I didn't have say anybody in the 50s I think I do but if I didn't have anyone in the 50s I still would have to list the five here because these have to be evenly spaced everything all right where those ones came from so this the stems are the first digits in this example and so now I'm going to easily organize these into groups I'm going to put them in the right places so this nine we said was a zero nine so it goes with the zero so I'm going to put the 9 here it goes with this guy the 15 is a one and a five so the one here and the five goes here 25 so that goes with the 2 and then the five I went all right how I know where to put these yes the six need to go before I'm not there yet but it will yes the answer is yes but I'm not doing it um 47s right now I'm just going across my list putting the leaves on my plot here okay oh I'm just putting each of these numbers that's actually why I listed them to make sure I didn't forget any of them so I've now put those numbers up there so it's not going to skip the three I'm just putting my list onto this chart I'm glad you asked though other questions on how I'm putting those here yes he wants to know what to do with the 16. that's exactly where we are wait a minute we already have a five there you you might have a long list of numbers on this one digit so he wants them how to put the 16 there's already a five here we just put the six right next to it whoa I have left no commas just right next to kind of evenly spaced kind of think of these as columns so this tells me if I hadn't looked up here this tells me there's a 15 and a 16 in my list same thing with the six right the six is a zero six so I would just put it over here you want to make sure you evenly space these when you put them in there you don't want to squish some of them together and spread some out I'll talk about why in a few minutes so there's the six the 28 would go here place because I keep stopping the top other questions on how I'm putting those on there make sure you ask me a question now I'm about to have you finish it everyone knows how to put the rest of those numbers on here well what about the 32 would you put it in the first column yes so that everyone hear a question the 32 is the first one that goes with the three so you always start on the left is keep filling them in as you go so the 32 will go there they only just keep moving over columns if you have more of them so do me a favor see if you can put the rest of them on there you're done already that's what happens I start talking to people like I've already done Joe some people were listening though I'm not writing for those of you who are we're not done yet see if you can fit all those numbers on there yeah while you're doing that I'm going to put them on here real quick and we'll see if we agree hopefully I copied the list down right we'll find out if my lens doesn't agree with yours here I agree with yours I could have made a mistake so if you're just different than mine just let me know so we got so this kind of tells me a lot of information already this tells me right now I've got five numbers that you know five people who are under the age of ten at their ages right I've got two people that are in their teens two teenagers four people in their 20s I have just as many people in my 40s as I do that are under 10 because I have five people in this list and five people in this list which is why you want to keep them evenly spaced so you can tell when they're the same length so here's the bad news that's not a standpoint it's almost a standpoint which is what Cristiano's question was about to be a stem plot it's almost like this except your leaves have to be in order so that's why I gave you two lines here this is my scratch paper to get started now I'm just going to come over here recopy my stems and then put each list each row in order from the smallest to biggest if you can do that all in one step good for you but it's hard to find the smallest one we need to move things over if you miss it so for me it's actually easier to make one here and then reorder it to get to my answer so I'm gonna put these in order from smallest to biggest [Music] putting two or three numbers in order is a lot easier than putting 22 numbers in order these were all in order already so this die right here is my stem book it has the stems it has the leaves everything's in order depends on that here's what we love about stem Puffs number one it takes a long list of data and puts it into a nice compact space if I if I give you one of these they can on the next test if I do do a stem part and say what numbers are listed in the table could you tell me if you didn't know what they looked like up here could you read it off of here yeah yeah right this one represents a 40 and a 41 and a 45. so you could take them off so it's all the numbers in a nice compact space if I asked you for the smallest number could you find it the biggest number you could find it and you don't have to search it's like oh wait I missed one there's another one bigger or smaller the longer the less the harder it is to find things like that in it could you find the one right in the middle right in the middle if you had to hmm I want to find one right in the middle yes could you like add like the smallest number and biggest number and divide by two I actually wanted the exact number that was in the middle of all these if I had so you're that's a good estimate though I like your idea but there might be a number like right in the middle where half people are younger and how people are older yes maybe if you go up the middle column like go to the floor and then go to the middle number in the floor so I like our thinking is that the middle how many people are older than 45. one two three four five six how many are younger than 45 a lot more than six I might well think you know that's good though yes if you just count from the top and the bottom we could count from the top and bottom until they meet we could count how many there are just take half of it turns out there's 22 if you count them so by counting to the top of the bottom I might go 11 down like two three four five six seven eight nine ten there's eleven right there from the top if I did 11 from the bottom I'd be so this is 11 from the top is 11 from the bottom so I went backwards right what'd you say I didn't hear you never mind she was thinking but I didn't like it say it again it's between 28 and 32. which I think is what you said just didn't trust yourself we don't have one number right in the middle but do we agree that half the people are 28 and younger and half the people are 32 and older so halfway between those would be 30. so 30 would be the number that half the people are younger and half the people are older we're going to learn that later it's called the median it's actually chapter three terminology but because they're in order here we can actually even find that where am I just given you this list and said hey figure out what number is exactly the one that half of people are older and half are younger good luck finding out looking at this list I don't know if I would have come up with 30 looking at it so this organizes a lot