Statistics Stemplots

Hi and welcome to www.educator.com.0000

Today we are going to be talking about stem plots.0002

We are going to talk about stem plots because they are another kind of visualization.0007

What sets them apart from other kinds of ways that you could visualize a distribution.0011

What do they look like and how did we construct one.0016

I should say upfront that stem plots are not frequently used but they are sometimes used in tests and classes.0019

They are frequently mentioned in textbooks which is I’m covering in a lesson.0028

If you are working with very large data sets, stem plots would not be very useful to you.0035

If you are actually trying to work with data, you might want to get this lesson.0040

What sets stem plots apart?0048

Let us think about this.0051

When we look at data sets, those rows and rows of data, they include the exact values but it does not show us the distribution visually.0053

It is almost impossible to see the distribution.0063

The nice thing about dot plots and histograms is that it shows you the distribution visually.0067

You could see the shape, the center and how spread out it is.0072

Unfortunately they do not always show the exact values.0079

Sometimes dot plots do but only if you have very small range.0083

Stem plots are a way of grouping the values yet it includes the exact values so it is nice.0090

It is between the dot plots and histograms, you can group them together and bin them together0106

but you will still see the exact values and it shows you the distributions visually.0112

What do stem plots actually look like?0120

Here is our first example.0122

They are also called stem and leaf plots.0124

The stems are the tens digit and the leaves are the ones digit of your data.0128

Let us take this class.0137

Let us say it is a physics class and here are the test grades for all these people.0138

I have put it already in order, from the least to the greatest.0144

Couple of people are really doing poorly in this class, actually more that half.0151

These people are doing well but they are facing to be a minority.0157

Let us get it into our stem plot.0162

On a stem plot we put the tens in one column.0164

The tens that we have are 2, 3, 4, 5, 6, 7, 8, 9 and here are the ones numbers.0168

What I have taken, I will put it in a different color.0177

I have taken this number and I have split it apart into 2 and 0.0181

Now I look at the next set, there are 3 people who scored in the 30’s but I’m missing one of them.0185

It should be 0 and 7 and 8.0195

Let us look at all those people who scored in the 40’s which looks like this is the majority.0202

I will put the 0, 0, 2, 2, 5, 5, 8, 8 and then let us look at those score in the 50’s.0209

There is one person who scored 50 and one person who scored 52 and 67.0222

I will put the 6 here and the 7 here.0231

For the 70’s there are 3 people, I will put the 2, 7, 8.0235

The ones places.0241

For the 80’s there are two people, the 0 and 8.0243

For the 90’s there is just one person who got 97.0247

When you look at the stem plot, to read each of these values you cannot read this as 3,078.0252

You have to read this as the 30, 37, and 38.0260

This is a 40, 40, 42, 42, 45, 45, 48, 48.0268

When you look over here you could see a distribution.0274

If you imagine totaling this over on the side you would see that this is a right skewed distribution.0281

That is the stem and leaf plot looks like.0297

The other thing you could do is you could create back to back stem plots.0303

You could use the same stem but with the leaves coming off either side of it.0307

In this way you could compare two distributions at once.0311

Let us say in the same physics class, someone is interested in whether it helps to have had calculus before.0315

Because calculus is the math that underlies physics.0321

We have put all the people who have not taken calculus before, the no’s and put them up here.0325

We have put all the people who have taken calculus before down here.0334

Now let us put in a stem plot.0339

The stems are going to be the same, 2, 3, 4, 5, 6, 7, 8 and 9 but let us start with the no calculus distribution.0342

Here we have somebody who scored 30 and nobody scored at the 20’s.0351

Here is a 30.0358

Here are two people who scored in the 40’s.0360

Here is one person who scored in the 50’s.0369

This very high performer has also not taken calculus before.0374

That is surprising.0379

Let us look at these people who have taken calculus before.0381

Here is one person in the 20’s, right there.0384

Two people who scored in the 30’s, 37 and 38.0388

Lots of people who scored in the 40’s, 40, 40, 42, 45, 45, and 48.0393

One person who scored in the 50’s. 52.0402

One person who scored in the 60’s.0405

Three people who scored in the 70’s, 72, 77, 78.0408

And two people who scored in their 80’s 80 and 88.0414

Let us put the distribution.0420

Here the distribution seems to be something like this.0422

Here the distribution definitely looks similar, they are both right skewed distributions.0430

Remember, right skewed means that a tail is with the high values.0440

That is how we know that they are right skewed even though right now it seems that they are down skewed or south skewed.0459

Let us start from scratch and try to create our stem plots.0470

Here these are cross grades, persons from the same class and it goes up to 50 but let us see.0473

There is all these scores here but they are not in any particular order.0480

Right now it seems like there is 20 but then it goes to 20.0485

This will be hard to create a stem plot because all the values are in different order.0491

What is helpful in creating a stem plot is putting this data into the right order first.0495

Here is that same data that has been sorted.0503

It seems like we have 10, 20, 30 up to 40.0508

Let us start the stem and I will put my stem in blue.0513

Let me put my stem over on one side because it is going to be a one sided stem and leaf plot.0522

1, 2, 3, 4.0528

I will put my leaves in red.0535

From ones I need to put 11, 13, 15.0538

For the 20’s I need to put 22, 23, 28, and 29.0545

For the 30’s I need 30, 30, 33, 33, 34, 34, 6, 7, and 8.0555

Perfect.0567

For the 40’s I need 0, 4, 4, 8, and 9.0570

There is our stem plot.0577

Our stem plot looks like that.0580

I cannot quite tell.0585

There are still few values here.0587

These are tough to see the distribution.0590

It could be normal, uniform, even.0592

Let us go on.0597