Basic Math Histograms

Welcome back to Educator.com.0000

For the next lesson, we are going to go over histograms.0002

A histogram is a bar graph that shows the frequency data that occurs within intervals.0006

It looks like almost identical to a bar graph.0016

It pretty much is a bar graph; but the difference is that the bar graph...0018

it just shows you the relationship between two different variables, two different things.0025

We know a bar graph looks like this.0035

Something like that where this represents something and this represents something.0043

A histogram is almost identical to that except a histogram shows the frequency.0049

It shows how many times something occurs, how frequent something occurs.0058

And it is also going to be within intervals.0065

On this side, this horizontal side right here, this is going to show the intervals.0070

This right here is going to show the frequency, how many times.0078

Let's say I have a set of numbers; I just have my data.0084

It is going to be 7, 11, 1, 12, 5, and 14.0089

I have six numbers.0100

The first thing I want to do to create a histogram is to find what I want my intervals to be in.0104

I am going to set intervals here.0113

Meaning it is going to be numbers between 1 and 5, then 6 and 10, then so on.0116

You are going to create the groups.0125

For this, let's say I am going to do exactly that.0128

It is going to be 1 through 5; my interval is going to be 1 through 5.0132

Then 6 through 10; then 11 through 15; it is going to be every five.0136

Let's say I am going to do 1.0141

From here to here is going to be 1 through 5.0144

Then from here to here, it is going to be 6 through 10.0149

Then from here to here, it is going to be 11 through 15.0154

Another thing about histograms is that the bars that you are going to draw, they are going to be stuck together.0160

There is not going to be any space in between them like the bar graph because it is in intervals.0170

All the numbers are going to fall in between one of these numbers.0176

All the bars are going to be stuck together.0180

Here it is going to be the frequency.0185

This is the frequency, how many times those numbers occur.0190

Step one was to create the intervals.0198

Then what I want to do just to make things a little bit easier for me to graph,0201

let's tally up how many times the numbers fall into their intervals.0208

I am going to just do 1 through 5... write my intervals... 6 through 10, 11 through 15.0215

Let's say I am going to tally up.0223

Every time a number falls under that category, that group, I am going to tally it up.0228

7, the first one, is right there; that is a tally mark for this group.0233

11, it is going to fall under there; 1 is going to fall here.0239

12 here; 5 here; and 14 is going to be there.0243

The frequency from this group 1 through 5 is going to be just two.0252

6 through 10 is going to be just once; 11 through 15 is three.0257

The frequency, here I am going to just do one, two, three, four.0262

One, two, three, four because the most I see a group is going to be is three.0271

That is the most; now all I have to do is create my bars.0279

The first one, 1 through 5, what is the frequency for that?--two.0284

I am going to graph that; I can shade it in.0290

The next group, 6 through 10, is just once.0303

It is going to be like that.0310

My third group frequency, three times; I go up to three; shade that in.0320

That is it; that is your histogram.0339

Again the first thing you do when you have a set of data like that,0343

the first thing you want to do is look at your data, look at your numbers and decide on your intervals.0347

How do you want to group up those numbers?0354

Once you do that, tally up how many times those numbers fall into that group.0357

Once you do that, you are going to create your intervals here,0364

create the frequency here, and then you are just going to draw your bars.0368

That is a histogram.0372

The first example, we are going to draw a histogram for the frequency table.0376

Here it gives us the intervals and the frequency.0380

All we have to do is draw the histogram.0383

Remember that this right here, the horizontal part of it, we are going to create the intervals.0390

I have four different groups, four intervals; one, two, three, and four.0400

This will be 1 through 4; this will be 5 through 8; 9 through 12; 13 through 16.0410

The frequency is going to be here; look at the biggest number is eight.0421

Then I know I have to show up to 8 on this part right here.0426

It will be 1, 2, 3, 4, 5, 6, 7, 8.0432

This is eight; 1, 2, 3, 4, 5, 6, 7, 8.0441

1 through 4, 1 through 4, the frequency is five.0449

I am going to go all the way up to five.0454

The next one is 5 through 8; 5 through 8 is three; go up to three.0463

Next one is eight; 9 through 12, the interval is eight; up to eight.0477

I don't have any more colors so I am just going to use black again.0498

13 through 16 is seven; go up to seven.0502

It would be nice if you have a ruler, you can draw these straight lines.0515

That is it; that is the histogram; again interval is the frequency.0522

The age of each child that attended the summer camp is given.0529

Create a histogram of the data.0532

We have all the ages of the children that attended the summer camp.0535

Again the first step is to create your intervals.0542

You want to create how you want to group up the eight, all the numbers.0545

It is really up to you.0551

If you want to create more intervals, then you can make the groups smaller.0551

You can make numbers for each group smaller.0556

Or if you want to create less than intervals, then you have to make the groups a little bit larger.0562

To create the interval, you want to look at the biggest number.0569

The biggest number here or this case the oldest child is 17.0575

The smallest number here is 2; youngest is 2; the oldest is 17.0583

You have to create your intervals based on those numbers.0588

Let's see, I want to create my intervals in every five.0594

Let's say 1 through 5, then 6 through 10, 11 through 15, 16 through 20.0600

Remember whenever you create your intervals, make sure that each interval has to be the same.0612

It has to be the same for each number of numbers for each group.0618

1 through 5 and then see here.0624

It is 1 through 5 and then through 10 and then through 15 and then through 20.0626

I know that is the same for each group.0631

Next step once you create your intervals is to see how many fall under each group.0635

Let's tally up the numbers; 5 is going to go into this group.0643

11 is going to fall under 11 through 15.0648

3 is right there; 9 in there; 6 is going to go right there.0652

7 in there; 8; 15; 10.0660

Once you have four, just make that the fifth one.0669

4 in there; 14, 10, 5, 8, 17, 14, 2, 2, 12, and 12 right there.0676

I have 5, 10, 15, 16, 17, 18 numbers total.0706

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18.0711

Now that I have my intervals and I have the frequency of each interval, I can create my histogram.0718

Just draw that; and then you are going to draw that.0726

These numbers here are going to be the age.0732

This is going to be the frequency.0740

I am going to need four intervals.0751

It is 1 through 5, then 6 through 10, three, and four.0753

6 through 10, 11 through 15, 16 through 20.0763

Here the most that occurs, this one, seven.0773

I know I have to list out up to seven.0777

One, two, three, four, five, six, seven, eight.0782

Here is seven; one, two, three, four, five, six, seven, eight.0789

The first one, 1 through 5, that interval I have five; draw up to five.0797

The next one is seven; up to seven.0812

11 through 15, another five; I am going to use black again.0827

16 through 20, the last one is just only one person that falls under that age group.0840

That is it; that is your histogram.0852

The next one, create a histogram of the following test scores.0858

We have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, twelve scores.0863

For this one, I probably want to create my intervals maybe in tens.0871

50, I know that my smallest number is 50 here.0882

My biggest number that I see is 96.0886

Because these are test scores, it will help me see how many fall under...0891

how many scored within the 50s and the 60, 70s, 80s, 90s.0895

Let's just create our intervals; 50 through 59.0900

Then 60 through 69; 70 through 79; 80 to 89; then 90 to 99.0907

The first one, 50, right there; 56; 82.0928

Again the first thing I did was create my intervals to see0937

how many groups and how many numbers will fall under each group.0941

Now I am taking the numbers in the data.0946

I am going to tally it into the groups to see the frequency of each interval.0948

The next one is 79, 71, 65, 90, 85, 83, 64, 96, 92.0956

This way I can see that means if you scored within 50 to 59, that is an F.0987

Two Fs; this is a D; two Ds; two Cs; three Bs; and three As.0994

That is good; we have majority of the scores being Bs and As.0999

This helps you see; it helps you see how many of each there are.1006

Once you have this done, you can go ahead and create your histogram.1012

Going to make this a little longer.1022

I have five intervals, five groups.1028

It is going to be first right there; two, three, four, five.1031

This will be 50 through 59; 60 through 69; 70 through 79... 90 through 99.1040

These are all the scores; label that scores.1058

This right here is always going to be the frequency.1062

Here the group that occurs the most is three.1073

One of these, just three; one, two, three.1077

Or I just always like to do one more than I need; one, two, three, four.1083

Let's just create our bars now; the first group, 50 to 59 is two.1091

You are going to draw the bar up to two.1096

The next one, 60 to 69 is two; also two; two.1104

The next one is also two; two Cs; the Bs, we have three of them.1120

I only have three colors so I am going to go back to black; go up to three.1133

Then I am going to use blue again; 90 to 99, the As, three of them.1145

That is our histogram.1160

That way we can see our data a little bit clearer rather than when they are listed out like that.1161

If they are like this, then I can see since these are all the different scores,1167

F, D, C, B, A, I can see how frequent each of them are.1172

That is the whole point of the histogram.1177

That is it for this lesson; thank you for watching Educator.com.1180