Statistics Bar Graphs

Welcome back to www.educator.com.0000

Today we are going to be covering bar graphs.0002

Today’s roadmap looks like this, first we are going to review all the frequency distributions that we have done so.0010

Then we are going to talk about a little bit about bar graphs and how they are different.0017

Mainly is that they involve categorical variables and looking at the frequency of each value.0020

Then we are going to contrast bar graphs and histograms because they are going to0026

look very similar to each other but they are very different ideas underlying them.0030

But they look superficially similar.0036

We are going to talk about whether shape applies to bar graphs, central tendency instead as well.0038

First let us review all the frequency distributions we have done so far.0048

What was on the Y axis?0052

Well since they are frequency distributions, largely it is something like frequency.0054

Sometimes you will see frequency distributions that have relative frequency and that does not change the shape, center, or spread.0060

Because you are basically just dividing by a constant.0072

What was on that X axis?0075

Remember in all of our histograms, dot plots, and stem plot so far, it is usually on the X axis.0078

In the case of stem plots in that sort of Y axis, that central column that is going to be the values of the variable, whatever your variable is.0086

So far we have looked at variables such as height, number of friends, photos, number of photos, those kind of variables.0105

We have each of those variables and we have all the values for that variable on the X axis.0128

Let us look at the different types of frequency visualizations we have looked at so far.0137

You could think of them as graphs or charts.0146

We have covered dot plots, remember what those look like?0154

They look like little dots or stars.0158

We have looked at histograms which look like bars, those are pretty frequent.0163

We have looked at stem and leaf plots that have the actual numbers in them like 2, 3, 4 and then they have 0 – 5, 0 – 2.0171

We are going to look at bar graphs.0184

When I draw a bar graph, which one does this look like?0186

It looks very similar to the histograms, right.0194

Here is the difference, so far in all three of these kinds here the variable of interest has always been continuous.0198

There is something in between 62 inches and 63 inches, right?0220

Like having 100 friends and 101 friends.0227

It is meaningful having 101 friends, having one more friend.0233

These have been interval, they have ratio values and so these variables have largely been continuous.0238

In bar graphs, I will color this red so that you know it is different.0248

In bar graphs, for the first time we are going to be looking at variables that are categorical.0258

If you recall categorical means that these variables are going to be like little bins, right?0268

There is nothing in between 1 and 2, in the case of categorical variables0276

and these are going to be largely useful for things that are nominal measures.0283

Things like gender having been male or female.0288

There are some things in between male and female but for the purposes of statistics we treat as a categorical variable.0291

They are nothing in between hair color, you either have black hair or brownish hair or blondish hair rates and reddish hair, other colors.0301

There is nothing in between eye color.0315

It is not a continuo necessarily.0318

Because of that categorical variables are going to be visualized in a very different way.0321

These visualizations are going to be called bar graphs.0328

Let us go ahead and look at an example of the bar graph.0335

They basically look like histograms superficially but the way you could tell is by looking at the X axis.0338

This is how you can be able to tell whether it is a histogram or bar graph because on the X axis you should see a categorical variable.0349

Let us look at an example.0361

If you put up the Excel file that you could download, here we have all of these variables in these columns.0365

Each of our cases is one of our people from www.facebook.com, these are our 100 friends from www.facebook.com.0373

Let us go down to the column that says relationship status, here it is.0381

Here is relationship status.0387

This is something that www.facebook.com really big for, because all of a sudden you could internet stalk people0389

and figure out what their relationship status is.0395

But here what we see is relationship status is a whole bunch of numbers.0398

If you click on the variables sheet, it will tell you what those numbers stand for.0404

Relationship status is in column H and we are going to color this in red fonts so you could clearly follow along.0410

If you scroll to the right it tells you that it is a nominal kind of measure and it is a categorical variable.0419

Perfect for doing bar graphs.0425

Here is what the dummy coding looks like.0427

Although they are numbers there, those numbers do not actually stand for numbers.0430

They are just dummy codes because they are stand ins for nominal names, nominal categories.0434

Here it says if there is a 0 in that column, it just means that the relationship status is left blank or unfilled in.0443

If they have a 1 it means that they are single.0451

If it is a 2, they are in a relationship.0455

If it is a 3, they are engaged.0458

If it is a 4, they are married.0461

If it is a 5, it is complicated.0463

If it is a 6, they just put something else.0466

We know that they have 0 through 6 as the potential values that could be in that variable.0470

Let us go to the relationship status sheet.0478

Here I have already filled in the category labels for you and the status is that they would have.0482

Let us make a frequency table, this is going to look the same as before.0488

Let us go ahead and put in our formula, the equal sign (=) first for the function count if.0492

I want Excel to count this person and if they have a blank in their relationship status.0501

I will put in a comma because I know I’m going to need that.0515

Here is my data and I know this is going to stay put if I put in dollar sign ($).0520

I’m going to lock it in place and that just tells me what sheet we are in.0529

Count in this data if it meets this criteria of 0.0538

I’m going to close my parentheses.0547

There are 13 people out of our 100 that have left their relationship status blank.0550

I’m just going to copy and paste all of that down and we see that just from looking at our frequency table,0557

We could see that most of the people in our sample are single or in a relationship, not too serious.0561

Here we will select all of these before we meet the bar graphs.0573

The reason of selecting these category labels is that when I select them, Excel will just fill it in for me.0581

It will fill in that X axis for me.0588

I’m going to click on charts and go ahead and click on column.0592

And here we go.0598

I’m going to delete that because it is redundant.0603

Here we have a nice bar graph.0607

Notice that it looks almost exactly like a histogram but one of the difference is that in bar graphs0612

there are spaces in between to indicate that these are separate bins that cannot be continuously looked at.0618

Because of that we see that here we see the same information as we saw in the frequency table that being single is the most frequent category.0627

Being in a relationship is the second most frequent.0640

These are all much less frequent and it is a little common to leave a blank but not too common.0643

That is one example of a bar graph.0653

It looks just like histograms but the difference was we used categorical variable.0660

Let us take our example that I have just copied and pasted it on here and let us look at whether sheet, center,0670

or spread of distributions that we have looked at before apply to bar graphs.0678

Now let us think about this, can we really say that this is a skewed right sheet? that it has a tail?0683

Let us think about this.0695

Well, in order to answer that question we might want to think about this idea, will it matter if the order of the bars were reversed?0697

Let us say I decided to put the people who left it blank over here and people who said it is complicated.0705

I have decided to dummy code that as number 1 right.0712

And let us say I decided to switch single, married, and in a relationship with engaged.0717

I will switch all of those.0724

It would look like a left skewed distribution.0726