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Lecture Comments (6)

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.

Box-and-Whisker Plot

Related Links

  • 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 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

Transcription: Box-and-Whisker Plot

Welcome back to

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