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