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

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

## Discussion

## Study Guides

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## Table of Contents

## Transcription

## Related Books

### Histograms

#### Related Links

- Histogram: A bar graph that shows the frequency data that occurs within intervals

### Histograms

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
- Histograms 0:05
- Definition and Example
- Extra Example 1: Draw a Histogram for the Frequency Table 6:14
- Extra Example 2: Create a Histogram of the Data 8:48
- Extra Example 3: Create a Histogram of the Following Test Scores 14:17

### Basic Math Online Course

### Transcription: 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 see*0937

*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

1 answer

Last reply by: Amha Bekele

Sun Feb 1, 2015 7:27 PM

Post by Ken Mullin on January 23, 2012

There is no mention of class marks and class boundaries or even midpoints.

Is this because the video is directed toward much younger students who might be confused by the lexicon and arithmetic involved?