Simplify Your Workflow: Search MiniWebtool.
Add Extension
Home Page > Math > Statistics And Data Analysis > Five Number Summary Calculator

Five Number Summary Calculator

Calculate the five-number summary (minimum, Q1, median, Q3, maximum) for any dataset. Features an interactive box-and-whisker plot, step-by-step quartile calculations, outlier detection, and multiple calculation methods.

Five Number Summary Calculator
โšก Quick Examples:
Separate values with commas, spaces, semicolons, or new lines. Minimum 4 values required.

Embed Five Number Summary Calculator Widget

About Five Number Summary Calculator

The Five Number Summary Calculator computes the five key descriptive statistics that summarize any dataset: the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. This tool generates an interactive box-and-whisker plot, detects outliers automatically, and provides step-by-step calculations with three different quartile methods to match your textbook or software.

What is a Five-Number Summary?

A five-number summary is a set of five descriptive statistics that divide a dataset into four equal parts (quartiles). Together, these five values provide a comprehensive snapshot of how data is distributed, including its center, spread, and range. The five-number summary is the foundation of the box-and-whisker plot, one of the most widely used statistical visualizations.

Five-Number Summary
{Minimum, Q1, Median, Q3, Maximum}

The Five Numbers Explained

StatisticDescriptionPercentile
MinimumThe smallest value in the dataset0th percentile
Q1 (First Quartile)The median of the lower half; 25% of data falls below this value25th percentile
Median (Q2)The middle value; divides the dataset in half50th percentile
Q3 (Third Quartile)The median of the upper half; 75% of data falls below this value75th percentile
MaximumThe largest value in the dataset100th percentile

How to Calculate a Five-Number Summary

  1. Sort the data in ascending order from smallest to largest.
  2. Find the minimum (first value) and maximum (last value).
  3. Find the median (Q2): For an odd number of values, it is the middle value. For an even number, it is the average of the two middle values.
  4. Find Q1: The median of the lower half of the data (values below the overall median).
  5. Find Q3: The median of the upper half of the data (values above the overall median).

Example Calculation

Dataset: 3, 7, 8, 5, 12, 14, 21, 13, 18

Sorted: 3, 5, 7, 8, 12, 13, 14, 18, 21

Five-Number Summary: {3, 6, 12, 16, 21}

Understanding the Box-and-Whisker Plot

A box-and-whisker plot (box plot) is the visual representation of the five-number summary:

Box plots are valuable for comparing distributions between groups, identifying skewness, and spotting outliers at a glance.

Quartile Calculation Methods

Different textbooks and software use different methods to calculate Q1 and Q3. This calculator supports three methods:

MethodDescriptionUsed By
ExclusiveExcludes the median when splitting data into halves (odd n). Most common textbook method.Most statistics textbooks, TI calculators
InclusiveIncludes the median in both halves (odd n). Also known as Tukey's hinges.Some textbooks, certain software
InterpolationUses linear interpolation at the 25th and 75th percentile positions.Excel PERCENTILE.INC, Python numpy, R default

For even-sized datasets, the exclusive and inclusive methods produce identical results. Differences appear only with odd-sized datasets.

Outlier Detection with IQR

The 1.5ร—IQR rule is the standard method for identifying outliers:

Outlier Fences
Lower Fence = Q1 โˆ’ 1.5 ร— IQR   |   Upper Fence = Q3 + 1.5 ร— IQR

How to Use This Calculator

  1. Enter your data: Type or paste your numbers into the input field, separated by commas, spaces, semicolons, or new lines. You can also click a quick example to get started.
  2. Choose a method: Select the quartile calculation method that matches your textbook or software requirements.
  3. Click Calculate: Press the "Calculate Five-Number Summary" button to see results.
  4. Review results: Explore the five-number summary cards, interactive box plot, method comparison, outlier analysis, step-by-step breakdown, and sorted data visualization.

Frequently Asked Questions

What is a five-number summary?

A five-number summary consists of five descriptive statistics that divide a dataset into four equal parts: the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. It provides a concise overview of the data distribution and is the foundation for box-and-whisker plots.

What is the difference between exclusive and inclusive quartile methods?

The exclusive method (standard textbook) excludes the median from both halves when calculating Q1 and Q3. The inclusive method (Tukey's hinges) includes the median in both halves for odd-sized datasets. For even-sized datasets, both methods produce the same result. The exclusive method is more commonly taught in statistics courses.

How are outliers detected using the five-number summary?

Outliers are detected using the 1.5ร—IQR rule. Any value below Q1 โˆ’ 1.5ร—IQR or above Q3 + 1.5ร—IQR is considered a mild outlier. Values beyond 3ร—IQR from the quartiles are extreme outliers. The IQR (interquartile range) is Q3 โˆ’ Q1.

What is a box-and-whisker plot?

A box-and-whisker plot (box plot) is a graphical representation of the five-number summary. The box spans from Q1 to Q3, with a line at the median. Whiskers extend to the most extreme non-outlier values. Individual outlier points are plotted beyond the whiskers. It visually shows data spread, skewness, and outliers.

How do you calculate the interquartile range (IQR)?

The interquartile range (IQR) is calculated as Q3 minus Q1. It represents the spread of the middle 50% of the data. The IQR is resistant to outliers, making it a robust measure of variability compared to the range or standard deviation.

Reference this content, page, or tool as:

"Five Number Summary Calculator" at https://MiniWebtool.com/five-number-summary-calculator/ from MiniWebtool, https://MiniWebtool.com/

by miniwebtool team. Updated: Mar 21, 2026

Developer API available: Run this tool from your app, automation, or agent with one JSON HTTP request. View API docs

You can also try our AI Math Solver GPT to solve your math problems through natural language question and answer.

Related MiniWebtools:

AI Content DetectorNew
AI Token CounterNew
Box and Whisker Plot Maker
Character Counter
Multiplication Table GeneratorNew
Number Pattern FinderNew
Percentile CalculatorNew
Quartile Calculator
Rounding CalculatorNew
Significant Figures CalculatorNew

Statistics And Data Analysis:

Top & Updated:

Random PickerRandom Name PickerInstagram User ID LookupImage ResizerLine CounterFPS ConverterSort NumbersRelative Standard Deviation CalculatorBatting Average CalculatorMAC Address GeneratorRemove SpacesFacebook User ID LookupERA CalculatorWord to Phone Number ConverterRandom Truth or Dare GeneratorSum CalculatorMAC Address LookupRandom Quote GeneratorFeet and Inches to Cm ConverterSun, Moon & Rising Sign Calculator ๐ŸŒž๐ŸŒ™โœจSlope and Grade CalculatorPercent Off CalculatorInvisible Text Generator๐Ÿ“ท OCR / Image to Textโฌ› Aspect Ratio CalculatorMercury Retrograde CalendarOPS CalculatorNumber of Digits CalculatorSHA256 Hash GeneratorVertical Jump CalculatorRandom Superpower GeneratorAudio SplitterMP3 LooperSquare Root (โˆš) CalculatorMerge VideosRoman Numerals ConverterRandom IMEI GeneratorRandom Birthday GeneratorLog Base 10 CalculatorBitwise CalculatorCm to Feet and Inches ConverterRandom Credit Card GeneratorSaturn Return CalculatorRandom Activity GeneratorSalary Conversion CalculatorRandom Fake Address GeneratorYouTube Channel StatisticsOn Base Percentage CalculatorHalfway Date CalculatorFile Size ConverterMaster Number CalculatorCaffeine Overdose CalculatorRandom Meal GeneratorAI Text HumanizerCompound Growth CalculatorWord Ladder GeneratorPhone Number ExtractorRandom Poker Hand GeneratorRandom Writing Prompt GeneratorSlugging Percentage CalculatorCompare Two StringsBattery Life CalculatorText FormatterStair CalculatorBinary to Gray Code ConverterNumber to Word ConverterWAR CalculatorWeight Loss Calculator๐Ÿ–ฑ๏ธ Click CounterIP Subnet CalculatorRandom Movie PickerAdd Text to ImageLottery Number GeneratorOctal Calculator๐Ÿ“… Date CalculatorRandom Group GeneratorRandom Loadout GeneratorProportion CalculatorSun Position CalculatorVideo CompressorDay of the Year Calculator - What Day of the Year Is It Today?Image SplitterPercent Growth Rate CalculatorBreak Line by CharactersGray Code to Binary ConverterSHA512 Hash GeneratorBCD to Decimal ConverterVideo to Image ExtractorLeap Years ListYouTube Tag ExtractorDecimal to BCD ConverterLove Compatibility CalculatorWord Scramble GeneratorPerfect Number CheckerCM to Inches ConverterArc Length CalculatorBingo Card GeneratorRandom Emoji GeneratorTime Duration CalculatorFirst n Digits of PiRemove Lines Containing...Number ExtractorBcrypt Hash Generator / CheckerConnect the Dots GeneratorAcreage CalculatorWHIP CalculatorRandom User-Agent GeneratorHebrew Calendar ConverterQuotient and Remainder CalculatorList of Prime NumbersAI Punctuation AdderMartingale Strategy CalculatorCone Flat Pattern (Template) GeneratorSocial Media Username CheckerEmail ExtractorSmall Text Generator โฝแถœแต’แต–สธ โฟ แต–แตƒหขแต—แต‰โพLong Division CalculatorRatio to Percentage CalculatorRandom Time GeneratorRemove Leading Trailing SpacesWhat is my Zodiac Sign?IP Address to Hex ConverterModulo CalculatorURL ExtractorBinary to BCD ConverterAstrological Element Balance CalculatorBolt Torque CalculatorDay of Year Calendar๐ŸŽฐ Gacha Pity CalculatorBroken Link CheckerPER CalculatorAPI TesterVideo SplitterFlip VideoAI Language DetectorLunar Calendar ConverterWhat is my Lucky Number?Random Tournament Bracket GeneratorSort Lines AlphabeticallySteel Weight CalculatorRatio CalculatorMandelbrot Set Explorer๐Ÿ” Plagiarism CheckerLinear Programming SolverRemove AccentList RandomizerImage CompressorSum of Positive Integers CalculatorSourdough CalculatorColor InverterYouTube Comment PickerAdjust Video SpeedMolarity CalculatorMD5 Hash Generator1099 Tax CalculatorAI ParaphraserHeight Percentile CalculatorRandom Chess Opening GeneratorMultiple Fraction CalculatorAdd Prefix and Suffix to TextHTML Compressor๐Ÿ”Š Tone GeneratorRandom Line PickerOutlier CalculatorCollage MakerRemove Audio from VideoRMD CalculatorNumber RandomizerPercentage Increase CalculatorRandomize NumbersJob FinderFraction CalculatorMAC Address AnalyzerCoin FlipperPercentile CalculatorBoxing Punch Power CalculatorHypotenuse CalculatorRandom PIN GeneratorBeer Chill Time CalculatorBoiling Point CalculatorMiter Angle CalculatorPVIF CalculatorRandom Number PickerAngel Number CalculatorRandom Math Problem GeneratorFence CalculatorRandom Excuse GeneratorTrigonometric Equation SolverArithmetic Sequence CalculatorPercent to PPM ConverterTessellation GeneratorTwitter/X Timestamp ConverterName Number CalculatorAmortization CalculatorName RandomizerPVIFA CalculatorRandom Chord GeneratorHVAC Sizing CalculatorHex to BCD ConverterBCD to Binary ConverterBCD to Hex ConverterMedian CalculatorStandard Error CalculatorAverage CalculatorReverse VideoActual Cash Value CalculatorScientific Notation to Decimal ConverterLog Base 2 CalculatorRoot Mean Square CalculatorSHA3-256 Hash GeneratorAI Sentence ExpanderLbs to Kg ConverterHex to Decimal ConverterConvolution CalculatorRandom String GeneratorMarkup CalculatorDecimal to Hex ConverterInstagram Font GeneratorSocial Media Image Size GuideTikTok Money CalculatorTwitter/X Character CounterYouTube Watch Time CalculatorTwitch Earnings CalculatorYouTube Shorts Monetization CalculatorFacebook Ad Cost CalculatorSocial Media ROI CalculatorSocial Media Post Time OptimizerCTR CalculatorROAS CalculatorInfluencer ROI CalculatorForce CalculatorAcceleration CalculatorVelocity CalculatorMomentum CalculatorProjectile Motion CalculatorKinetic Energy CalculatorPotential Energy CalculatorWork and Power CalculatorDensity CalculatorPressure CalculatorIdeal Gas Law CalculatorFree Fall CalculatorTorque CalculatorHorsepower CalculatorDilution CalculatorChemical Equation BalancerStoichiometry CalculatorPercent Yield CalculatorEmpirical Formula CalculatorTitration CalculatorMole/Gram/Particle ConverterIrregular Polygon Area CalculatorFrustum CalculatorTorus Calculator3D Distance CalculatorGreat Circle Distance CalculatorCircumscribed Circle (Circumcircle) CalculatorInscribed Circle (Incircle) CalculatorAngle Bisector CalculatorTangent Line to Circle CalculatorHeron's Formula CalculatorCoordinate Geometry Distance CalculatorVolume of Revolution CalculatorSurface of Revolution CalculatorParametric Curve GrapherRiemann Sum CalculatorTrapezoidal Rule CalculatorSimpson's Rule CalculatorImproper Integral CalculatorL'Hรดpital's Rule CalculatorMaclaurin Series CalculatorPower Series CalculatorSeries Convergence Test CalculatorInfinite Series Sum CalculatorAverage Rate of Change CalculatorInstantaneous Rate of Change CalculatorRelated Rates SolverOptimization Calculator (Calculus)Gradient Calculator (Multivariable)Divergence CalculatorCurl CalculatorLine Integral CalculatorSurface Integral CalculatorJacobian Matrix CalculatorNewton's Method CalculatorRREF Calculator (Row Echelon Form)Matrix Inverse CalculatorMatrix Multiplication CalculatorDot Product CalculatorCross Product CalculatorVector Magnitude CalculatorUnit Vector CalculatorAngle Between Vectors CalculatorNull Space CalculatorColumn Space CalculatorCramer's Rule CalculatorMatrix Diagonalization CalculatorQR Decomposition CalculatorCholesky Decomposition CalculatorMatrix Power CalculatorCharacteristic Polynomial CalculatorBayes' Theorem CalculatorF-Test / F-Distribution CalculatorHypergeometric Distribution CalculatorNegative Binomial Distribution CalculatorGeometric Distribution CalculatorExponential Distribution CalculatorWeibull Distribution CalculatorBeta Distribution CalculatorSpearman Rank Correlation CalculatorFisher's Exact Test CalculatorContingency Table CalculatorOdds Ratio CalculatorROT13 Encoder/DecoderAtbash Cipher ToolVigenรจre Cipher ToolPronunciation IPA ConverterHemingway-Style Readability EditorSentence Length Variance AnalyzerWord Frequency AnalyzerBusiness Days CalculatorAdd Business Days to DateDate Pattern GeneratorHow Long Until CalculatorHow Long Ago CalculatorBirthday Across Cultures CalculatorHijri Calendar ConverterInsulin Sensitivity Factor CalculatorCarb-to-Insulin Ratio CalculatorLean Body Mass to Strength CalculatorOne-Mile Walk Test (Rockport) CalculatorCooper 12-Minute Run CalculatorFFMI CalculatorAPGAR Score CalculatorGlasgow Coma Scale CalculatorWells Score Calculator (DVT/PE)Tennis Score TrackerSoccer xG (Expected Goals) CalculatorCricket Run Rate CalculatorRugby Points CalculatorRace Time PredictorSwimming SWOLF CalculatorYoga Pose Hold TimerFishing Knot Strength CalculatorBike Gear Ratio CalculatorClimbing Grade ConverterWine Pairing SuggesterStandard Drink CalculatorCaffeine Half-Life TrackerSpice Substitution FinderDietary Restriction Recipe FilterMarinade Time CalculatorFermentation Time CalculatorSmoking Wood Pairing GuideFreelance Project Pricing CalculatorSaaS Pricing CalculatorSubscription Cost TrackerSide Hustle ROI CalculatorRemote Work Savings CalculatorCoffee Habit Cost CalculatorGym vs Home Workout Cost CalculatorLunch Cost CalculatorWealth Growth Visualizer1031 Exchange CalculatorRental Yield CalculatorCash-on-Cash Return CalculatorBRRRR Method CalculatorSection 8 Rent CalculatorRoommate Rent SplitterAirbnb Pricing OptimizerStatute of Limitations CalculatorSentence Reduction CalculatorSales Tax Nexus CheckerPatent Filing Fee CalculatorTrademark Class FinderWill Asset Distribution CalculatorWorkers' Compensation CalculatorStopping Distance CalculatorTrip Cost SplitterVehicle Weight Distribution CalculatorTrailer Tongue Weight CalculatorTire Tread Wear CalculatorEngine Compression Ratio CalculatorHeadlight Beam Distance CalculatorCat Litter Box CalculatorAquarium Heater Wattage CalculatorBird Cage Size CalculatorReptile Habitat UVB CalculatorPet Travel Crate Size FinderHorse Hay CalculatorCrochet Hook Size ConverterKnitting Needle Size ConverterKnitting Pattern CalculatorCross-Stitch Floss CalculatorQuilt Binding CalculatorOrigami Paper Size CalculatorPottery Clay Shrinkage CalculatorBeading Pattern CalculatorResin Casting Volume CalculatorEmbroidery Thread Length CalculatorHiking Pace Calculator (Naismith's Rule)Backpacking Food Weight CalculatorTent Footprint Size CalculatorSleeping Bag Temperature Rating GuideKnot Tying Reference ToolStar Visibility CalculatorTide Time CalculatorReynolds Number CalculatorBernoulli Equation CalculatorHeat Transfer CalculatorThermal Expansion CalculatorSpecific Heat Capacity CalculatorGear Ratio Calculator (Mechanical)Pulley System CalculatorHydraulic Cylinder Force CalculatorBelt Length CalculatorCloset Capsule CalculatorStorage Unit Size CalculatorMoving Box Quantity CalculatorGift Card Tip CalculatorGas vs Electric Cost ComparisonPrint Cost CalculatorHair Dye Mixing CalculatorLaundry Detergent Dosage CalculatorDishwasher Load OptimizerTile Grout CalculatorPaint Color Mixing CalculatorFlashcard Spaced Repetition SchedulerLearning Curve CalculatorCornell Notes GeneratorVocabulary Quiz GeneratorLanguage Learning Hours to Fluency CalculatorCollege Cost CalculatorScholarship ROI CalculatorAI Recipe Generator (From Ingredients)AI Gift Idea GeneratorAI Meal Plan GeneratorAI Workout Plan GeneratorAI Reading List GeneratorAI Travel Itinerary GeneratorAI Excuse Generator (Polite)AI Apology Letter WriterAI Unit Converter (Natural Language)AI Resume / CV AnalyzerAI Text Tone AnalyzerAI Data Visualizer (Paste CSV)AI Regex GeneratorAI SQL Query GeneratorPaycheck Calculator (Take-Home Pay)VA Loan CalculatorARM Mortgage CalculatorBiweekly Mortgage Payment CalculatorPMI CalculatorMortgage Points CalculatorBalloon Loan CalculatorInterest-Only Mortgage CalculatorConstruction Loan CalculatorLand Loan CalculatorBoat Loan CalculatorRV Loan CalculatorMotorcycle Loan CalculatorCar Affordability CalculatorOut-the-Door Price CalculatorRent Affordability CalculatorProrated Rent CalculatorRent Increase CalculatorMileage Reimbursement CalculatorPer Diem CalculatorInvoice GeneratorSalary Raise CalculatorSeverance Pay CalculatorHSA Calculator529 College Savings CalculatorI Bond CalculatorT-Bill CalculatorCD Ladder CalculatorCredit Utilization CalculatorLoan Comparison CalculatorGross-Up CalculatorSWP CalculatorRD CalculatorPPF CalculatorEPF CalculatorNPS CalculatorGratuity CalculatorHRA Exemption CalculatorUK Stamp Duty CalculatorZakat CalculatorTithe CalculatorBetting Odds ConverterPayPal Fee CalculatorStripe Fee CalculatorEtsy Fee CalculatoreBay Fee CalculatorAmazon FBA CalculatorShopify Profit CalculatorWholesale Price CalculatorCraft Pricing Calculator