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Feb 17, 2023

2 pages

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... Show more

box-and
a graphical representation of data
smallest and largest values
lower and upper anartiles.
median
KEY FEATURES:
best drawn
smallest
v

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:

  1. Find the median Q2Q2 = 30
  2. Calculate Q1 = 28 and Q3 = 46
  3. Identify the minimum 99 and maximum 5050 values
  4. 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 = Q1+Q3Q1 + Q3 / 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 9trips9 trips: 2, 3, 3, 6, 8, 10, 11, 12, 13 Females 11trips11 trips: 1, 3, 4, 5, 11, 12, 13, 16, 23, 31, 51

Example: To compare these datasets:

  1. Create separate box and whisker plots for males and females
  2. Use the same scale for both plots to allow direct comparison
  3. 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.

box-and
a graphical representation of data
smallest and largest values
lower and upper anartiles.
median
KEY FEATURES:
best drawn
smallest
v

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:

  1. Smallest value lowerwhiskerlower whisker
  2. Q1 lowerquartilelower quartile
  3. Q2 medianmedian
  4. Q3 upperquartileupper quartile
  5. Largest value upperwhiskerupper whisker

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 IQRIQR = 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:

  1. Positive Skew: Q3 - Q2 > Q2 - Q1
  2. Negative Skew: Q3 - Q2 < Q2 - Q1
  3. 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.



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

 

Statistics

160

Feb 17, 2023

2 pages

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

box-and
a graphical representation of data
smallest and largest values
lower and upper anartiles.
median
KEY FEATURES:
best drawn
smallest
v

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

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:

  1. Find the median Q2Q2 = 30
  2. Calculate Q1 = 28 and Q3 = 46
  3. Identify the minimum 99 and maximum 5050 values
  4. 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 = Q1+Q3Q1 + Q3 / 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 9trips9 trips: 2, 3, 3, 6, 8, 10, 11, 12, 13 Females 11trips11 trips: 1, 3, 4, 5, 11, 12, 13, 16, 23, 31, 51

Example: To compare these datasets:

  1. Create separate box and whisker plots for males and females
  2. Use the same scale for both plots to allow direct comparison
  3. 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.

box-and
a graphical representation of data
smallest and largest values
lower and upper anartiles.
median
KEY FEATURES:
best drawn
smallest
v

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:

  1. Smallest value lowerwhiskerlower whisker
  2. Q1 lowerquartilelower quartile
  3. Q2 medianmedian
  4. Q3 upperquartileupper quartile
  5. Largest value upperwhiskerupper whisker

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 IQRIQR = 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:

  1. Positive Skew: Q3 - Q2 > Q2 - Q1
  2. Negative Skew: Q3 - Q2 < Q2 - Q1
  3. 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.

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