Basic Math 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