How To Find The Five Number Summary In Statistics - WikiHow

Skip to ContentQuizzes

• PRO Courses Hot Guides Tech Help Pro Expert Videos About wikiHow Pro Upgrade
• QUIZZES All Quizzes Hot Love Quizzes Personality Quizzes Trivia Quizzes Taylor Swift Quizzes
• EDIT Edit this Article
• EXPLORE Tech Help ProAbout UsRandom ArticleQuizzes Request a New ArticleCommunity DashboardTrendingForums Arts and EntertainmentArtworkBooksMoviesComputers and ElectronicsComputersPhone SkillsTechnology HacksHealthMen's HealthMental HealthWomen's HealthRelationshipsDatingLoveRelationship Issues Hobbies and CraftsCraftsDrawingGamesEducation & CommunicationCommunication SkillsPersonal DevelopmentStudyingPersonal Care and StyleFashionHair CarePersonal Hygiene Quizzes Love Quizzes Personality Quizzes Fun Games Arts and EntertainmentFinance and BusinessHome and GardenRelationship Quizzes Cars & Other VehiclesFood and EntertainingPersonal Care and StyleSports and Fitness Computers and ElectronicsHealthPets and AnimalsTravel Education & CommunicationHobbies and CraftsPhilosophy and ReligionWork World Family LifeHolidays and TraditionsRelationshipsYouth
• LOG IN

  Log in

  Social login does not work in incognito and private browsers. Please log in with your username or email to continue. Facebook Google wikiHow Account No account yet? Create an account
• RANDOM

• Home
• Random
• Browse Articles
• TrendingNew
• Quizzes & Games
• All QuizzesHot
• Love Quizzes
• Personality Quizzes
• Fun Games
• Dating Simulator
• Learn Something New
• Forums
• Courses
• Happiness Hub
• Explore More
• Support wikiHow
• About wikiHow

• Log in / Sign up

Terms of Use wikiHow is where trusted research and expert knowledge come together. Learn why people trust wikiHow

• Categories
• Education and Communications
• Studying
• Mathematics

How to Find the Five Number Summary in Statistics Download Article Reviewed by Joseph Meyer

Last Updated: February 24, 2025

Download Article

• Preparing the Data for Calculation
|
• Finding the Minimum and Maximum
|
• Calculating the First Quartile
|
• Find the Median
|
• Calculate the Upper Quartile
|
• Completing the 5 Number Summary
|
• Video

|Show more |Show less X

This article was reviewed by Joseph Meyer. Joseph Meyer is a High School Math Teacher based in Pittsburgh, Pennsylvania. He is an educator at City Charter High School, where he has been teaching for over 7 years. Joseph is also the founder of Sandbox Math, an online learning community dedicated to helping students succeed in Algebra. His site is set apart by its focus on fostering genuine comprehension through step-by-step understanding (instead of just getting the correct final answer), enabling learners to identify and overcome misunderstandings and confidently take on any test they face. He received his MA in Physics from Case Western Reserve University and his BA in Physics from Baldwin Wallace University. This article has been viewed 61,217 times.

The five number summary is an important way of organizing data to show statistical importance through dispersion. This summary consists of the minimum, Quartile 1 (Q1), median (Q2), Quartile 3 (Q3), and the maximum; usually organized in that specific order on a box plot. The lower quartile (Q1) consists of the lower 25% of the data while the upper quartile (Q3) contains 25% of the highest numbers in the data set or 75% of the entire data. This statistical analysis is very useful for larger data because the median identifies the center of the data, the minimum and maximum gives the length of the data and the quartiles allows for further analysis of an assortment. [1]

Steps

Part 1 Part 1 of 6:

Preparing the Data for Calculation

Download Article

1. 1 Determine the amount of numbers in your data set. You can do this by counting all of the numbers in the data set.
   • Example: In a data set 1,3,4,5,11,12,14,20,11,2 there are 10 numbers in the data set
2. 2 Organize the data in increasing order. Starting with the smallest number value up to the largest number.
   • Organize the data by scanning and writing down the numbers in increasing number.
   • While scanning cross out the numbers that were already used to keep track
   • Example: In a data set 1,3,4,5,11,12,14,20,11,2 the numbers would be organized as 1,2,3,4,5,11,11,12,14,20
   Advertisement
3. 3 Write down or memorize the equations for both quartiles and the median.
   • The 1st Quartie equation ¼ (n+1)
   • The median equation ½(n+1)
   • The 3rd Quartile ¾(n+1)
Advertisement

Part 2 Part 2 of 6:

Finding the Minimum and Maximum

Download Article

1. 1 Find the smallest and the largest numbers of the total data set. In a data set organized in increasing order the minimum is the first number and the maximum in the last number.
   • Example: In a data set 1,2,3,4,5,11,11,12,12,14,20 (organized in increasing order) the minimum is 1 (lowest) and maximum is 20 (largest).

Part 3 Part 3 of 6:

Calculating the First Quartile

Download Article

1. 1 Plug in the value of n in the First Quartile formula. ¼(n+1)
   • Example: In a data set 1,2,3,4,5,11,11,12,14,20 n=10, the equation will be ¼(10+1)
2. 2 Solve the equation: Solving the equation will not give the exact answer of Quartile 1, it will instead give the position of the number.
   • Example: In a data set 1,2,3,4,5,11,11,12,14,20 n=10, the equation will be ¼(10+1) which equals 11/4 or 2.75. This means that the first Quartile is located at position 2.75 in the data set.
3. 3 Use the solution from the equation to find the number at that position. After solving the equation, use the answer to find the location in the data set where the quartile is located.
   • Example: In a data set 1,2,3,4,5,11,11,12,14,20 because the equation gave the decimal 2.75, the 1st Quartile is located between the 2nd and 3rd numbers in the data set
4. 4 Find the average of the numbers to the left and to the right of the position.If a decimal is calculated
   • A decimal means that the quartile is located in between the two numbers located left and right of it.
   • Add the left and right numbers together then divide by two
   • Example: In a data set 1,2,3,4,5,11,11,12,14,20 the number is in the 2.75th position which is between the 2nd and 3rd numbers meaning we take (2+3) then divide by 2 which equals 2.5[2]
Advertisement

Part 4 Part 4 of 6:

Find the Median

Download Article

1. 1 Plug in the value of n into the Median formula. ½(n+1)
   • Example: In a data set 1,2,3,4,5,11,11,12,14,20 n=10, The equation will be ½(10+1)
2. 2 Solve the equation. Solving the equation will give you the location of the number (median) in the data set.
   • Example: In a data set 1,2,3,4,5,11,11,12,14,20 n=10, The equation ½(10+1) will equal 5.5, which places the median at position 5.5
3. 3 Locate the median in the data set. Use the position received from solving the median equation to locate the data.
4. 4 Find the average of the numbers right and left of the value received from the equation if it is an even number of data.
   • Example: In a data set 1,2,3,4,5,11,11,12,14,20 n=10 the median is located position 5.5 which is between the 5th and 6th number. To find the median we will take the average of the 5th and 6th numbers. Taking the average means adding the two numbers together and dividing by 2.
   • Example: 1,2,3,4,5,11,11,12,14,20 the numbers beside 5.5 is 5 and 11 therefore the equation goes (5+11)/2=8. The Median then equals 8.
5. 5 If it is an odd number of data then the position given by the equation will be the exact position of the median.
   • Example:#*Example: In a data set 1,2,3,4,5,11,11,12,14,20,20 n=11, plug 11 in equation ½(11+1) the median will be at position 6 so the median is 11.
Advertisement

Part 5 Part 5 of 6:

Calculate the Upper Quartile

Download Article

1. 1 Plug in the value of n in the Third Quartile formula. ¾ (n+1)
   • Example: In a data set 1,2,3,4,5,11,11,12,14,20 n=10, The equation will be ¾ (10+1)
2. 2 Solve the equation. The solving of the equation will not give the 3rd Quartile it will instead give the position of the number.
   • Example: In a data set 1,2,3,4,5,11,11,12,14,20 n=10, The equation will be ¾ (10+1) will equal 33/4 .This means that the third Quartile is located at position 8.25.
3. 3 Use the solution from the equation to find the number at the position. After computing the equation use the answer to find the location in the data set where the quartile is located.
   • Example: In a data set 1,2,3,4,5,11,11,12,14,20 the number is in the 8.25th position, therefore, the 3rd Quartile is between the 8th and 10th numbers
4. 4 Find the average of the numbers to the left and the right of the position if a decimal is calculated from the equation.
   • Add the left and right numbers together then divide by two.
   • Example: In a data set 1,2,3,4,5,11,11,12,14,20 the number is in the 8.25th position which is between the 8th and 10th numbers meaning we take (12+14) then divide by 2 which equals 13
Advertisement

Part 6 Part 6 of 6:

Completing the 5 Number Summary

Download Article

1. 1 Write down the 5 number summary using commas to separate them. Use the order minimum, 1st Quartile, Median, 3rd Quartile, Maximum.
   • Doing this will help differentiate each part of the data
   • Example: In a data set 1,2,3,4,5,11,11,12,14,20 the 5 number summary will be 1,2.5,8,13,20

Expert Q&A

Search Add New Question Ask a Question 200 characters left Include your email address to get a message when this question is answered. Submit Advertisement

Video

Tips

Submit a Tip All tip submissions are carefully reviewed before being published Name Please provide your name and last initial Submit Thanks for submitting a tip for review!

You Might Also Like

How toFind the IQR How toCalculate the Upper Quartile How to Create a Box and Whisker Plot How to Find the Median and Mean of a Histogram + Examples How toCalculate Outliers How toCalculate Cumulative Frequency How toCalculate Quartiles in Excel How toCalculate Average or Mean of Consecutive Numbers How toFind Mode, Median, Mean and Range How toFind Mean, Median, and Mode How toFind the Mode of a Set of Numbers Finding Class Width for a Frequency Distribution Table How toCalculate Precision How to Calculate Midrange with a Formula or in Excel Advertisement

References

1. ↑ https://www150.statcan.gc.ca/n1/edu/power-pouvoir/ch12/5214877-eng.htm
2. ↑ https://www.purplemath.com/modules/boxwhisk2.htm

About This Article

Reviewed by: Joseph Meyer Math Teacher This article was reviewed by Joseph Meyer. Joseph Meyer is a High School Math Teacher based in Pittsburgh, Pennsylvania. He is an educator at City Charter High School, where he has been teaching for over 7 years. Joseph is also the founder of Sandbox Math, an online learning community dedicated to helping students succeed in Algebra. His site is set apart by its focus on fostering genuine comprehension through step-by-step understanding (instead of just getting the correct final answer), enabling learners to identify and overcome misunderstandings and confidently take on any test they face. He received his MA in Physics from Case Western Reserve University and his BA in Physics from Baldwin Wallace University. This article has been viewed 61,217 times. 16 votes - 54% Co-authors: 7 Updated: February 24, 2025 Views: 61,217 Categories: Mathematics

• Print
• Send fan mail to authors

Thanks to all authors for creating a page that has been read 61,217 times.

Did this article help you?

Yes No Advertisement Cookies make wikiHow better. By continuing to use our site, you agree to our cookie policy. Reviewed by: Joseph Meyer Math Teacher 16 votes - 54% Click a star to vote Co-authors: 7 Updated: February 24, 2025 Views: 61,217

Quizzes & Games

IQ TestTake QuizAm I a Genius QuizTake QuizMemory TestTake QuizIQ Test For KidsTake QuizAm I Smart QuizTake QuizAm I Smart? Find Out with This Quick Intelligence TestTake Quiz

You Might Also Like

How toFind the IQRHow toCalculate the Upper QuartileHow to Create a Box and Whisker PlotHow to Find the Median and Mean of a Histogram + Examples

Featured Articles

How toRemove Shorts from Search Results on YouTubeWhat Are the Korean Animal Face Types? (And Which Type Do You Have?)Being the Little Spoon While Cuddling: Is It Better Than the Big Spoon?115+ Funny “Get Well Soon” Messages to Make Someone Laugh110+ “Fun Facts” for Interviews, Introductions, & IcebreakersHow Long Would You Survive In A Zombie Apocalypse?

Trending Articles

Am I Autistic Quiz210+ Shower Thoughts: Funny, Deep, Weird & Mind-BlowingHow Sexual Am I QuizWhy Can't I Sleep QuizWhat's My Personality Based on My Song Choices QuizGuess My Deepest Secret Quiz

Featured Articles

How to Roast Someone in a Rap Battle (Plus the Best Bars of All Time)What Turns a Girl On? 31 Things to Try on Your PartnerLove AnalyzerSending Your Sweetie a Love Note? Here are 200+ Romantic IdeasHow toExercise Your BrainHow toBe a Fun Person to Hang out With

Featured Articles

What Does Your Morning Routine Say About You?How toDevelop Productive HabitsHow toPractice Self CareWhat Song Matches Your Life Right Now?Will 2026 Be Your Year? Reveal Your FutureUnderstanding the Most Attractive Face Shapes (& Determining Your Own)

Watch Articles

Amazing Super Bowl Party Ideas Guests Will Cheer ForHow toDevelop Listening SkillsHow toNot Lose Your GirlfriendHow to Draw an OwlHow toTreat AllergiesHow toIntroduce Friends to Other Friends

Trending Articles

Can We Guess If You're Single or Taken?What Would My Nickname Be QuizCan We Guess How Tall You Are Quiz5 Different Types of Butts: Find Your ShapeHow toBe PrettyKissing Tips: The wikiHow Guide to the Perfect Kiss

Quizzes & Games

What Age Is My Brain QuizTake QuizAm I Smarter than a 5th Grader QuizTake QuizQuick IQ TestTake QuizAccurate IQ Checker Quiz: How Smart Am I?Take QuizWhat Is My Numerology Number QuizTake QuizCognitive TestTake Quiz

• Categories
• Education and Communications
• Studying
• Mathematics

wikiHow Newsletter You're all set! Helpful how-tos delivered toyour inbox every week! Sign me up! By signing up you are agreeing to receive emails according to our privacy policy.

• Home
• About wikiHow
• Experts
• Jobs
• Contact Us
• Site Map
• Terms of Use
• Privacy Policy
• Do Not Sell or Share My Info
• Not Selling Info
• Contribute

Follow Us

×

Get all the best how-tos!

Sign up for wikiHow's weekly email newsletter

Subscribe You're all set! X --523