A comprehensive guide to box and whisker plots, covering... Show more
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Box and whisker plot
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Jun 30, 2025
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How to Draw a Box and Whisker Plot Step by Step Easy - Examples, Problems, and Tools
Practical Applications of Box and Whisker Plots
This page demonstrates how to apply box and whisker plot concepts to real-world data sets, providing examples of data analysis and interpretation.
Analyzing Student Marks
Let's examine a stem-and-leaf diagram showing marks out of 50 for 15 students:
0 | 1 2 3 5 5
1 |
2 | 4 5 8
3 | 0 1 1 7 9
4 | 3 5 6 8
5 | 0 0
Example: To create a box and whisker plot from this data:
- Find the median = 30
- Calculate Q1 = 28 and Q3 = 46
- Identify the minimum and maximum values
- Draw the plot on a scale from 0 to 50
Calculating Key Statistics
For this data set:
- Range = 50 - 9 = 41
- IQR = 46 - 28 = 18
Highlight: The large range and IQR suggest considerable spread in the student marks.
Interpreting Symmetry
In this example, the box is symmetric, meaning the median is equal to the mean of Q1 and Q2. This can be expressed as:
Q2 = / 2
Vocabulary: Symmetry in a box plot indicates that the data is evenly distributed around the median.
Comparing Male and Female Data
The page also includes an example comparing trip data for males and females:
Males : 2, 3, 3, 6, 8, 10, 11, 12, 13 Females : 1, 3, 4, 5, 11, 12, 13, 16, 23, 31, 51
Example: To compare these datasets:
- Create separate box and whisker plots for males and females
- Use the same scale for both plots to allow direct comparison
- Analyze differences in median, spread, and potential outliers
This comparison allows for a visual analysis of the differences in trip patterns between males and females, demonstrating the power of box and whisker plots in comparing distributions.
Understanding Box and Whisker Plots
A box and whisker plot, also known as a box plot, is a powerful tool for visualizing the distribution of data. This page introduces the key features and construction of these plots, as well as how to interpret them for data analysis.
Definition: A box and whisker plot is a graphical representation of data that displays the smallest and largest values, lower and upper quartiles, and the median.
Key Features of Box and Whisker Plots
Box and whisker plots are best drawn on graph paper and must include a scale. The main components are:
- Smallest value
- Q1
- Q2
- Q3
- Largest value
Example: In a sample plot, if Q1 = 3, Q2 = 6, Q3 = 9, the smallest value is 0, and the largest value is 15, the plot would show these key points along a scale.
Calculating Important Values
To construct a box and whisker plot, you need to calculate several key values:
- Range = Largest value - Smallest value
- Interquartile Range = Q3 - Q1
Highlight: The IQR is a crucial measure of spread in the data, representing the middle 50% of values.
Assessing Skewness
Box and whisker plots can reveal the skewness of a data set:
- Positive Skew: Q3 - Q2 > Q2 - Q1
- Negative Skew: Q3 - Q2 < Q2 - Q1
- Symmetrical: Q3 - Q2 ≈ Q2 - Q1
Vocabulary: Skewness refers to the asymmetry in a statistical distribution.
The relationship between measures of central tendency also indicates skewness:
- Positive Skew: Mode < Median < Mean
- Negative Skew: Mean < Median < Mode
Understanding these relationships is crucial for interpreting box plots skewness and making accurate data analyses.
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
You have the choice, we offer a 100% secure payment via PayPal or an Amazon gift card. There is no limit to how much you can earn.
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.9/5
App Store
4.8/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
How to Draw a Box and Whisker Plot Step by Step Easy - Examples, Problems, and Tools
A comprehensive guide to box and whisker plots, covering their construction, interpretation, and analysis of data skewness. This resource provides step-by-step instructions, examples, and key concepts for understanding and creating these statistical visualizations.
- Explains the components of a box... Show more
Practical Applications of Box and Whisker Plots
This page demonstrates how to apply box and whisker plot concepts to real-world data sets, providing examples of data analysis and interpretation.
Analyzing Student Marks
Let's examine a stem-and-leaf diagram showing marks out of 50 for 15 students:
0 | 1 2 3 5 5
1 |
2 | 4 5 8
3 | 0 1 1 7 9
4 | 3 5 6 8
5 | 0 0
Example: To create a box and whisker plot from this data:
- Find the median = 30
- Calculate Q1 = 28 and Q3 = 46
- Identify the minimum and maximum values
- Draw the plot on a scale from 0 to 50
Calculating Key Statistics
For this data set:
- Range = 50 - 9 = 41
- IQR = 46 - 28 = 18
Highlight: The large range and IQR suggest considerable spread in the student marks.
Interpreting Symmetry
In this example, the box is symmetric, meaning the median is equal to the mean of Q1 and Q2. This can be expressed as:
Q2 = / 2
Vocabulary: Symmetry in a box plot indicates that the data is evenly distributed around the median.
Comparing Male and Female Data
The page also includes an example comparing trip data for males and females:
Males : 2, 3, 3, 6, 8, 10, 11, 12, 13 Females : 1, 3, 4, 5, 11, 12, 13, 16, 23, 31, 51
Example: To compare these datasets:
- Create separate box and whisker plots for males and females
- Use the same scale for both plots to allow direct comparison
- Analyze differences in median, spread, and potential outliers
This comparison allows for a visual analysis of the differences in trip patterns between males and females, demonstrating the power of box and whisker plots in comparing distributions.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Understanding Box and Whisker Plots
A box and whisker plot, also known as a box plot, is a powerful tool for visualizing the distribution of data. This page introduces the key features and construction of these plots, as well as how to interpret them for data analysis.
Definition: A box and whisker plot is a graphical representation of data that displays the smallest and largest values, lower and upper quartiles, and the median.
Key Features of Box and Whisker Plots
Box and whisker plots are best drawn on graph paper and must include a scale. The main components are:
- Smallest value
- Q1
- Q2
- Q3
- Largest value
Example: In a sample plot, if Q1 = 3, Q2 = 6, Q3 = 9, the smallest value is 0, and the largest value is 15, the plot would show these key points along a scale.
Calculating Important Values
To construct a box and whisker plot, you need to calculate several key values:
- Range = Largest value - Smallest value
- Interquartile Range = Q3 - Q1
Highlight: The IQR is a crucial measure of spread in the data, representing the middle 50% of values.
Assessing Skewness
Box and whisker plots can reveal the skewness of a data set:
- Positive Skew: Q3 - Q2 > Q2 - Q1
- Negative Skew: Q3 - Q2 < Q2 - Q1
- Symmetrical: Q3 - Q2 ≈ Q2 - Q1
Vocabulary: Skewness refers to the asymmetry in a statistical distribution.
The relationship between measures of central tendency also indicates skewness:
- Positive Skew: Mode < Median < Mean
- Negative Skew: Mean < Median < Mode
Understanding these relationships is crucial for interpreting box plots skewness and making accurate data analyses.
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
You have the choice, we offer a 100% secure payment via PayPal or an Amazon gift card. There is no limit to how much you can earn.
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.9/5
App Store
4.8/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user