For more information, please see full course syllabus of Basic Math

For more information, please see full course syllabus of Basic Math

### Stem-and-Leaf Plots

#### Related Links

- Stemplot
- Statistics
- Quantitative data
- Information graphics
- Histogram
- Probability distribution
- Non-parametric statistics
- Data
- Median
- Mode

- Stem-and-leaf plot: Organizes data in order, so it is easy to see each item
- Stem: The digit(s) on the left, usually the tens digit
- Leaf: The digit on the right, usually the ones digit

### Stem-and-Leaf Plots

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- Stem-and-Leaf Plots 0:05
- Stem-and-Leaf Plots
- Extra Example 1: Use the Data to Create a Stem-and-Leaf Plot 2:28
- Extra Example 2: List All the Numbers in the Stem-and-Leaf Plot in Order From Least to Greatest 7:02
- Extra Example 3: Create a Stem-and-Leaf Plot of the Data & Find the Median and the Mode. 8:59

### Basic Math Online Course

### Transcription: Stem-and-Leaf Plots

*Welcome back to Educator.com.*0000

*For the next lesson, we are going to go over stem and leaf plots.*0002

*A stem and leaf plot is a way for you to organize your data so that it is easy to see.*0007

*It lists them out in order from least to greatest.*0015

*The stem of a stem and leaf plot is usually the tens digit.*0020

*It is the number on the left.*0027

*The leaf, red for the leaf, is the digit on the right which is the ones digit.*0031

*Let's say I have a number 52.*0039

*I am going to separate the number 52.*0044

*I am going to separate the digits into a stem and then a leaf.*0046

*The tens digit, the 5, I am going to make my stem.*0050

*The ones digit, my 2, is going to be my leaf; stem and leaf.*0057

*I am going to separate them by drawing a little line like that.*0063

*All the stems are going to go on the left side.*0069

*My leaves are going to go on the right side.*0071

*That is a number.*0074

*If I have these numbers here, I have 50, 52, and 55.*0075

*The stem, the tens digit, is all the same.*0088

*Since it is the same number, I am going to separate the stem and the leaves.*0093

*But I only have to write the stem one time because it is the same stem.*0098

*Then when I write my leaves, I am going to write the 0, the 2, and the 5.*0105

*It becomes 0, just like I separated this number 52.*0115

*Again because the stem is the same number,*0122

*I am going to just put the leaf, that 2, right there next to the 0.*0124

*Then again the next leaf, 5.*0130

*This represents the tens digit and then all the ones digits.*0134

*This is 50, 52, and then 55.*0139

*That is how you do a stem and leaf plot.*0145

*Using these numbers here, we are going to create a stem and leaf plot.*0151

*The first stem, the smallest stem that I see is the 1.*0157

*The smallest tens digit is the 1.*0164

*I have a 2; that is another stem.*0167

*I have a 3; I think that is it for my stems.*0170

*I am going to list out my stems; stems and my leaves; stem and leaf.*0175

*My stem, the smallest stem, 1; then 2; and then 3.*0186

*I don't think I have any more stems; that is it for my stems.*0195

*My leaves, the other side, I am going to write them out.*0200

*Before you do this, it will be a little bit easier... you don't have to do this.*0210

*But it is a little bit easier if you arrange your numbers in order from least to greatest.*0214

*Let's just do that; my smallest number here is 11.*0218

*Then it is 12; then 15; 18; let's see; then my twenties so it is 22; 25; 29.*0227

*Next is 30; 32; I have another 32; 33; and 39.*0260

*I have one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve.*0276

*One, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve.*0281

*I have all my numbers.*0285

*Now my stem, the 1, that is a tens digit; here is a tens digit.*0287

*Then my 1, my leaf here is going to be a 1.*0297

*This number here represents tens; ones; together, it becomes 11.*0302

*My next one, because it is the same stem, I am going to write it under here, the same stem.*0307

*The leaf here is 2 like that.*0312

*You don't have to write commas; just leave a little space; 1, 2.*0316

*Next is 5; the next leaf under the same stem is 8.*0320

*That is it for my ones, my tens digit right here.*0330

*Next is the 2, the 20s; that leaf is 2.*0336

*The next leaf is 5; next leaf is 9.*0344

*Moving on to the thirties, 3-0; 3-2; 3- another 2; 3-3; and 3-9.*0352

*This is the stem and leaf plot that represents all of these numbers here.*0369

*It represents my data; then I can see... what is my smallest number?*0372

*My smallest number with the smallest stem and the smallest leaf together is going to be 11.*0378

*My biggest number is going to be the biggest stem with the biggest leaf together is 39.*0385

*To find the median here, it doesn't ask me to find the median.*0392

*But I can find the median by eliminating because each leaf represents a number in the data.*0395

*I can just go ahead and eliminate starting from this.*0402

*This is the start; this is the last; the first and the last.*0405

*I can just start eliminating until I get to a middle number, till I get to a middle leaf.*0409

*Then I am going to use that stem and that leaf to create the median.*0415

*We are going to do that in the next example, example three.*0420

*Here we have a stem and leaf plot.*0427

*We have to list all the numbers in order from least to greatest.*0430

*It is like what we just did, except we are just going to do the opposite now.*0434

*Instead of creating the stem and leaf plot with our data,*0437

*we are going to use this to come up with our data, our list of numbers.*0441

*The smallest number here, this stem with this leaf.*0447

*This is the smallest leaf with the smallest stem, together makes 40.*0451

*That is my smallest number, 40.*0458

*My next is going to be 44; then 52; 55; 57; 58.*0460

*Here this is listed out because all the stems from 4 to 7 have to be listed out.*0475

*I don't have any leaves here with this stem.*0482

*There is no number here that is in my data.*0487

*I don't have sixties number.*0491

*Then I just move on to 71; 73; and then 73.*0495

*Notice, back to this 40, if I have a number 40, then I have to list out the 0 as my leaf.*0505

*Here be careful not to represent this as 60 because there is no 0 here.*0516

*Just because there is nothing there doesn't mean that you have a 60.*0524

*There has to be a 0 in order for you to have a 60 in your data.*0527

*This is it; these are all my numbers in this stem and leaf plot.*0532

*For this one, some chapter test scores are given.*0542

*Create a stem and leaf plot of the data.*0544

*Then find the median and the mode.*0546

*Again the first thing I want to do is list out my numbers in order from least to greatest.*0552

*These are all chapter tests; the lowest score is 40.*0556

*Then let's see, 48; 52; 67; 72; 83; and then... oh, I forgot 71.*0565

*Let me go back to here, 72, 83; 71, 72, and then 83.*0598

*After 83, 90... I forgot 79; back to 79.*0609

*Where was I?--83; after 83 is 90; 91; 98; and 100.*0624

*I have one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve.*0643

*One, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve.*0648

*I have all my numbers in order from least to greatest.*0652

*Now let's create our stem and leaf plot.*0657

*My stems and my leaf, going to separate like that; going to use black for this.*0660

*My smallest stem is a 4.*0671

*My biggest stem is going to be this number here.*0677

*Remember it is the numbers on the left.*0685

*My ones digit is going to be my leaf.*0687

*The remaining numbers to the left are going to be my stem.*0693

*It is going to be my stem.*0696

*Here I am going to separate this like that.*0698

*10 is going to be my stem; the 0 is going to be my leaf.*0700

*It is OK if you have more than one digit.*0704

*If you have two or three digits as your stem, that is fine.*0706

*4, 5, 6, 7, 8, 9, and 10; the leaf here is 0 and then 8.*0710

*For the next one, the stem is 5; the leaf is 2.*0727

*That is it for that.*0733

*Stem is 6; leaf is 7; here, stem 7, leaf 1; and 2 and 3.*0735

*This one's leaf is 3; for the nineties, 9-0; 9-1; 9-8.*0751

*For the last one, 10-0.*0762

*Those are all of the numbers represented in the stem and leaf plot.*0766

*I need to find my median and my mode; here let's see.*0773

*My median, because I know that the smallest stem with the smallest leaf is my smallest number in the data,*0784

*and then my biggest stem with the biggest... this right here, the last leaf is going to be my biggest number,*0792

*I know that I can start eliminating numbers from this right here and from the first and the last.*0801

*If I keep doing that, eliminate this and eliminate that.*0813

*The next one over is 48; the next one down from this is 98.*0816

*Then this; then this; then this; then this; then 71; then 83.*0822

*Then I have two numbers left in my data.*0832

*The whole point of doing this right now is to find the median.*0838

*I am trying to find the middle number.*0841

*Median is always middle; that is the keyword.*0842

*It has to be from order of least to greatest.*0846

*You can look for the median from here because we already listed them out.*0849

*But also be able to find the median from your stem and leaf plot.*0853

*This is the start; small stem with the first leaf all the way down to the biggest stem with the last leaf.*0859

*Start eliminating numbers until you get the middle; middle one or two middles.*0867

*In this case, because we have an even number of numbers,*0873

*we are going to have two numbers in the middle.*0876

*To find the median, we have to find the average of those two numbers.*0880

*For the median, it is going to be 2 plus the 9.*0885

*We are going to find the middle number between 2 and 9.*0893

*We are going to find the average or the mean between 2 and 9.*0896

*I am going to add them together and divided by 2.*0900

*2 plus 9 is 11; over 2.*0906

*To change this to a decimal, you can change it to a fraction or a decimal.*0912

*Remember that; 2, to change it to a mixed number...*0916

*This is called an improper fraction where the top number is bigger than the bottom number.*0920

*Let's change this to a mixed number.*0926

*2 fits into 11 how many times?*0928

*2 fits into 11 five times because that is going to make it a 10.*0931

*It only fits into it five times; that is our whole number.*0937

*How many leftovers do you have?--I have 1; over... keep that same denominator.*0940

*It is going to be 5 and 1/2.*0946

*To change this to a decimal, you are going to take the top number.*0949

*Place it inside like that; 2 on the outside.*0954

*You are going to put the decimal point at the end of that number.*0959

*Bring it up; 2 fits into 11 five times.*0963

*That gives us 10; subtract it; I get 1.*0968

*I am going to add a 0 at the end of this; bring that down.*0972

*2 goes into 10 five times; that gives us 10; subtract it; I get 0.*0976

*Your median is going to be either 5 and 1/2 as a fraction or 5.5 as a decimal.*0984

*It is just 5 and 1/2; that is the middle number between these two.*0992

*That is our median.*0996

*The mode, now mode, let's see.*0998

*Do we see any leaves written out twice for the same stem?*1002

*No, they are all different; I don't have a mode for this one.*1009

*Let's say for example, if I have another 8 right here,*1015

*then I know within the same stem, I have the same leaf written twice.*1019

*That would mean that I would have 98 and 98 again.*1024

*That would be my mode because remember the keyword for mode is most.*1028

*We are looking for any repeats, any numbers that occur more than one time.*1032

*Since I don't have any numbers that are repeating,*1042

*any numbers that are occurring more than once, I have no mode.*1045

*For mode, I am going to write none.*1050

*That is it for this lesson; thank you for watching Educator.com.*1059

1 answer

Last reply by: Professor Pyo

Thu Jan 2, 2014 5:29 PM

Post by Daniel Eckert on August 28, 2013

why is the Median 5.5? wouldn't it be 75.5?

0 answers

Post by Jaish Mishra on May 5, 2013

I don't really get extra example three.

0 answers

Post by Jeanette Akers on October 24, 2012

I've never studied Stem-and-Leaf plots before either, and I found this to be another GREAT visual lesson. And I totally get it and got it by watching this video one time. You are an awesome instructor. Thanks again!