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

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

### Box-and-Whisker Plot

#### Related Links

- Box-and-whisker plot
- Descriptive statistics
- Five-number summary
- Sample minimum
- Summary statistics
- Quartile
- Median
- Quartile
- Sample maximum
- Outlier
- Statistical population
- Statistical dispersion
- Data set

- Box-and-whisker graph: Displays the distribution of data items along a number line
- Shows the median, lower and upper quartiles, and lower and upper extremes

### Box-and-Whisker Plot

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
- Box-and-Whisker Plot
- Extra Example 1: Name the Median, Lower & Upper Quartile, Lower & Upper Extreme
- Extra Example 2: Draw a Box-and-Whisker Plot Given the Information
- Extra Example 3: Find the Median, Lower & Upper Quartile, Lower & Upper Extreme
- Extra Example 4: Draw a Box-and-Whiskers Plots for the Set of Data

- Intro 0:00
- Box-and-Whisker Plot 0:05
- Median, Lower & Upper Quartile, Lower & Upper Extreme
- Extra Example 1: Name the Median, Lower & Upper Quartile, Lower & Upper Extreme 6:04
- Extra Example 2: Draw a Box-and-Whisker Plot Given the Information 7:35
- Extra Example 3: Find the Median, Lower & Upper Quartile, Lower & Upper Extreme 9:31
- Extra Example 4: Draw a Box-and-Whiskers Plots for the Set of Data 12:50

### Basic Math Online Course

### Transcription: Box-and-Whisker Plot

*Welcome back to Educator.com.*0000

*For the next lesson, we are going to go over the box and whisker plot.*0002

*A box and whisker plot looks like this.*0009

*It displays the distribution of data items along a number line.*0012

*We are going to use the box and the whiskers to represent certain items in the data.*0018

*Before I explain this, I want to give you the data set.*0027

*The numbers that I am basing this plot on are 2, 3, 4, 5, 6, 7, and 9.*0032

*Let's say that that is my data set.*0051

*From here, I want to find the median.*0056

*Remember median; the key word for median is middle.*0061

*If the numbers are in order from least to greatest, then I want to find the middle number.*0065

*2, 3, 4, 5, 6, 7, and 9.*0069

*Let me just rewrite it here so I can give myself some room to work with... 6, 7, and 9.*0073

*To find the median, because it is in order from least to greatest, I can just find the middle number.*0083

*3 on this side; 3 on this side; that is my median.*0091

*This is called the median.*0095

*Not including the median, on the lower group of numbers,*0106

*the smaller group of numbers, I want to look for the median again.*0110

*Just from this group right here, just from those three numbers,*0115

*the median, the middle number, is going to be 3.*0119

*That number is called the lower... because it is part of the lower set... lower quartile.*0124

*Same thing for the other side.*0138

*Again between those three numbers, the median is going to be 7.*0141

*That is called your upper quartile.*0148

*All three numbers represent the median.*0157

*This 5 right here, that is the median within the whole set of numbers.*0161

*The lower quartile is the median among the lower half.*0167

*The upper quartile among the upper half.*0171

*The smallest number in your data which is the 2, that number there is called your lower extreme.*0179

*That means this number, the biggest number in your data, is going to be your upper extreme.*0194

*Again we have our median.*0208

*That is the first thing you want to look for, median.*0210

*From your lower half, you are going to find the median again.*0212

*That is your lower quartile; in the upper half, upper quartile.*0215

*Smallest number is your lower extreme.*0221

*Your largest number, the biggest number, is your upper extreme.*0224

*Once you find those numbers, we have five numbers circled there.*0227

*Those are the numbers that are going to be represented in this box and whisker plot.*0232

*The box right here, these three lines in the box,*0241

*this one, this one, and this one, represent your three medians.*0246

*The number right here, this right here is your median of the data.*0254

*This is your median; this right here which is 5; this your median.*0260

*These two right here, this one and this one, the 3 and the 7, are your quartiles.*0272

*This is the lower quartile; this one right here is your upper quartile.*0281

*Those three, your quartiles right here, that is what forms the box.*0293

*All you have to do is once you have the lower quartile,*0299

*you have the upper quartile, then you just draw lines connecting them like that.*0302

*That is how you create your box from the box and whisker plot.*0308

*These right here are called your whiskers.*0312

*Here is you whisker here; the whisker here.*0318

*This number right here is your lower extreme.*0321

*That is the 2; see how it is under the 2.*0330

*This one is your upper extreme.*0334

*That is how we form the box and whisker plot.*0341

*Median, your lower quartiles, that forms the box.*0344

*The whiskers are going to go to your extremes, the lower extreme and then the upper extreme.*0348

*Once you have a set of data, just look for those numbers.*0355

*Once you have them, you can just go ahead and just draw your box and your whiskers.*0358

*The first example, name the median, lower quartile, upper quartile, lower and upper extremes.*0365

*Remember within our box, we look for these numbers here.*0373

*This right here, this is your median.*0379

*The median I am going to say is 8.*0385

*This number here is my lower quartile; lower quartile is 6.*0396

*My upper quartile is 12.*0410

*Then your extremes, that number right there, the whiskers, is going to the 4.*0421

*My lower extreme is 4; my upper extreme is 13.*0428

*We got median, lower quartile, upper quartile, lower extreme, and upper extreme.*0446

*The next one, the information is given to us.*0457

*We just have to draw the box and whisker plot.*0462

*Remember the lower extreme and the upper extreme, that is my smallest number and my biggest number.*0466

*Those are the numbers that are going to be the numbers that my whiskers are going to be drawn to.*0472

*I know my lower extreme is going to go like that.*0482

*I am going to draw a point right there.*0486

*My upper extreme is going to be 12.*0488

*The easiest way to draw the box and whisker plot is to draw the box first.*0493

*My lower quartile is 5.*0499

*I am going to draw a little line like this on 5.*0504

*My upper quartile is 10; that is the median of the upper half.*0509

*Upper quartile is 10; draw line like that.*0516

*My median is 8; 8 right there.*0523

*Remember you want to draw your box; that is going to be the box.*0532

*You don't have to use it in different colors; it could just be like that.*0539

*Just make sure you have these three under the correct numbers.*0543

*Now you can just draw your whiskers.*0550

*From here, you can draw the whisker going out to the 4.*0553

*Here the whisker to the upper extreme; that is 12.*0558

*That is it; that is your box and whisker plot.*0565

*The next example, we are going to find the median,*0572

*the lower and the upper quartiles, the lower and the upper extremes.*0575

*Then we are going to graph it using the box and whisker plot.*0578

*The first thing to do since we have to find the median and the quartiles and the extremes,*0584

*I need to list my numbers out in order from least to greatest, the smallest number to the biggest number.*0592

*Smallest here is 5, then 6, then 7, 8, 8, 9, and 10.*0599

*Let's see, one, two, three, four, five, six, seven.*0613

*One, two, three, four, five, six, seven; just to make sure I didn't miss a number.*0615

*Then I need to find my median; let's see.*0620

*My median will be this right here; this is a median.*0627

*Then I want to find my quartiles.*0635

*Among these numbers, that will be the lower quartile.*0638

*This from here, there is my upper quartile.*0652

*Then my lower extreme; my upper extreme.*0660

*Now I need to graph the box and whiskers plot.*0680

*I need a number line first.*0685

*My largest number is 10 so I have to make sure I cover up to 10 on the number line.*0694

*1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.*0709

*My median is 8; draw a little line like that under 8.*0721

*My lower quartile is 6; my upper quartile is 9.*0729

*Once you have your three little lines right there, draw the box that connects those quartiles.*0739

*My lower extreme, from the box, I am going to draw a whisker out to that lower extreme, 5.*0749

*From here, whisker out to the upper extreme which is 10.*0757

*That is it for this one.*0765

*The fourth example, we are going to draw a box and whiskers plot for this set of data.*0769

*Again we are going to find the median.*0776

*The way we do that is to list numbers out from least to greatest.*0778

*The key word for median is middle.*0782

*Smallest number, 2; we got 2; then the 3; we have 4; another 4.*0787

*Then we have 6; then two 7s; 7, 7, 8, 9, 10, and 11.*0801

*I have one, two, three, four, five, six, seven, eight, nine, ten, eleven numbers.*0820

*One, two, three, four, five, six, seven, eight, nine, ten, eleven.*0825

*Now I need to look for my middle number, the median.*0830

*Let's see, one, two, three, four, five; we count five this way.*0835

*One, two, three, four, five; that leaves me with this number in the middle.*0838

*Remember if you have two numbers in the middle,*0845

*you have to find the average of those two numbers.*0850

*Let's say I had an extra number on this side.*0852

*6 and 7, if those were my middle numbers,*0857

*I would have to find the middle number between 6 and 7.*0859

*Again this is when you have an even number of numbers in your data.*0863

*Then your median, you have to find the middle number between the two numbers in the middle.*0868

*You can do that by adding those two numbers together and dividing it by 2.*0873

*You are finding the average, the mean, within those two numbers.*0877

*In this case, we have only one number so that is our median.*0881

*Then from the lower set of numbers, I look for my median again.*0890

*The middle number is 4; remember that becomes our lower quartile.*0900

*From the upper set, I have the 9; that is going to be my upper quartile.*0912

*My smallest number which is 2 is my lower is my extreme.*0928

*My largest number is my upper extreme.*0938

*Once I have those five numbers, I can draw my box and whiskers plot.*0947

*I am going to draw a number line.*0952

*My largest number is 11.*0962

*I have to make sure I cover up to 11 on this number line.*0964

*1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, one more, 12.*0968

*1, 2, 3, 4, 5, 6, 7...*0978

*I want to first draw my median.*0989

*On 7, I am going to draw that little line right there under 7.*0993

*Then your quartiles; the 4 like that; another one under 9.*0999

*Remember the quartiles are going to form your box.*1009

*Let's just draw a box like that.*1012

*Once you have your box, we need to draw our whiskers.*1021

*From this end, I am going to draw a whisker out to the lower extreme which is 2.*1025

*Draw a whisker out there.*1033

*On this side, my upper extreme is 11.*1038

*Draw the whisker out to 11 right there; that is it.*1041

*Remember these three are going to represent your medians.*1046

*This is the median of your data.*1051

*These two are the medians of the lower and upper halves.*1053

*That is going to form your box.*1057

*Your whiskers, draw it out to the lower extreme, the smallest number.*1059

*This whisker, upper extreme which is the largest number.*1064

*That is it for this lesson; thank you for watching Educator.com.*1069

3 answers

Last reply by: Professor Pyo

Sat Mar 2, 2013 12:53 AM

Post by Jeanette Akers on October 24, 2012

This a great visual presentation. I've never studied Box-and-Whisker Plots before. I find this lesson fascinating. No one could explain this material any better than you. Thanks.

1 answer

Last reply by: Mary Pyo

Fri Aug 19, 2011 11:58 PM

Post by julius mogyorossy on July 20, 2011

What would the lower and upper quartiles be if there were only four numbers left of median, and four to the right, what would this plot look like with an even amount of numbers.