Simplify Your Workflow: Search MiniWebtool.
Add Extension
Home Page > Math > Statistics And Data Analysis > Interquartile Range Calculator

Interquartile Range Calculator

Calculate the interquartile range (IQR), quartiles Q1, Q2, Q3, five-number summary, and detect outliers with interactive box plot visualization and step-by-step calculations.

Interquartile Range Calculator
Quick Examples
Enter at least 4 numbers. If your text has non-numeric content, use our Number Extractor first.

Embed Interquartile Range Calculator Widget

About Interquartile Range Calculator

The Interquartile Range Calculator computes the IQR, all quartiles (Q1, Q2, Q3), five-number summary, and automatically detects outliers in your dataset. With an interactive box plot visualization and step-by-step calculations, this tool helps you understand the spread and distribution of your data.

What is the Interquartile Range (IQR)?

The Interquartile Range (IQR) is a measure of statistical dispersion that represents the spread of the middle 50% of your data. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1):

Interquartile Range Formula
$$IQR = Q_3 - Q_1$$

Unlike the range (max - min), the IQR is resistant to outliers, making it a more robust measure of variability. It is widely used in descriptive statistics, data analysis, and for identifying outliers through the 1.5ร—IQR rule.

Understanding Quartiles

Quartiles divide a sorted dataset into four equal parts:

Five-Number Summary

The five-number summary provides a quick overview of a dataset's distribution:

  1. Minimum: The smallest value
  2. Q1: First quartile (25th percentile)
  3. Q2: Median (50th percentile)
  4. Q3: Third quartile (75th percentile)
  5. Maximum: The largest value

These five values are used to construct a box plot (box-and-whisker plot), which visually displays data distribution, skewness, and outliers.

Outlier Detection: The 1.5ร—IQR Rule

The IQR is commonly used to identify outliers using fences:

Outlier Fences
$$\text{Lower Fence} = Q_1 - 1.5 \times IQR$$ $$\text{Upper Fence} = Q_3 + 1.5 \times IQR$$

Data points falling below the lower fence or above the upper fence are considered potential outliers. For extreme outliers, the 3ร—IQR rule is used (values beyond Q1 - 3ร—IQR or Q3 + 3ร—IQR).

Quartile Calculation Methods

There are different methods for calculating quartiles, which may produce slightly different results:

MethodUsed ByDescription
ExclusiveTI-83/84, Moore & McCabe, Excel QUARTILE.EXCExcludes the median when calculating Q1 and Q3 for odd n. Most common in education.
InclusiveTI-85, Minitab, Excel QUARTILE.INCIncludes the median in both halves when calculating Q1 and Q3 for odd n.

This calculator supports both methods. The Exclusive method is more commonly taught in statistics courses and is the default.

How to Use This Calculator

  1. Enter your data: Input numbers separated by commas, spaces, or line breaks. You need at least 4 values.
  2. Select quartile method: Choose Exclusive (default, most common) or Inclusive based on your requirements.
  3. Set decimal precision: Select 2-15 decimal places for your results.
  4. Calculate: Click the button to see IQR, quartiles, five-number summary, outlier detection, box plot, and step-by-step calculations.

Applications of IQR

IQR vs Other Measures of Spread

MeasureSensitivity to OutliersBest Used When
IQRResistant (robust)Data may contain outliers; you want to describe typical spread
RangeVery sensitiveQuick overview; no outliers present
Standard DeviationSensitiveData is normally distributed; need precise variability measure
VarianceSensitiveStatistical calculations requiring squared deviations

Frequently Asked Questions

What is the Interquartile Range (IQR)?

The Interquartile Range (IQR) is a measure of statistical dispersion equal to the difference between the third quartile (Q3) and first quartile (Q1). It represents the spread of the middle 50% of your data and is calculated as IQR = Q3 - Q1. The IQR is resistant to outliers, making it a robust measure of variability.

How do you calculate the IQR?

To calculate the IQR: 1) Sort your data in ascending order. 2) Find Q1 (the median of the lower half). 3) Find Q3 (the median of the upper half). 4) Calculate IQR = Q3 - Q1. The result represents the range containing the middle 50% of your data.

What is the 1.5 IQR rule for outliers?

The 1.5 IQR rule identifies outliers as data points that fall below Q1 - 1.5ร—IQR (lower fence) or above Q3 + 1.5ร—IQR (upper fence). Points beyond these boundaries are considered potential outliers. The 3ร—IQR rule identifies extreme outliers.

What is the difference between Exclusive and Inclusive quartile methods?

The Exclusive method (used by TI-83/84, Moore & McCabe) excludes the median when calculating Q1 and Q3 for odd-sized datasets. The Inclusive method (used by TI-85, Minitab) includes the median in both halves. Both are valid; the Exclusive method is more common in education.

What is the five-number summary?

The five-number summary consists of: Minimum, Q1 (first quartile), Q2 (median), Q3 (third quartile), and Maximum. These five values provide a quick overview of your data's distribution and are used to construct box plots.

Why is IQR preferred over range for measuring spread?

IQR is preferred because it is resistant to outliers. The range (max - min) can be heavily influenced by extreme values, while IQR focuses on the middle 50% of data. This makes IQR a more robust and reliable measure of typical variability in a dataset.

Additional Resources

Reference this content, page, or tool as:

"Interquartile Range Calculator" at https://MiniWebtool.com/interquartile-range-calculator/ from MiniWebtool, https://MiniWebtool.com/

by miniwebtool team. Updated: Jan 27, 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
Angle Between Vectors CalculatorNew
Character Counter
Domain and Range Calculator
Function Grapher
Limit Calculator
Mean Median Mode Calculator
Range Calculator

Statistics And Data Analysis:

Top & Updated:

Random PickerRandom Name PickerInstagram User ID LookupImage ResizerLine CounterFPS ConverterSort NumbersRelative Standard Deviation CalculatorBatting Average CalculatorRemove SpacesMAC Address GeneratorFacebook User ID LookupERA CalculatorWord to Phone Number ConverterRandom Truth or Dare GeneratorFeet and Inches to Cm ConverterMAC Address LookupRandom Quote GeneratorSun, Moon & Rising Sign Calculator ๐ŸŒž๐ŸŒ™โœจSum CalculatorSlope and Grade CalculatorPercent Off CalculatorInvisible Text Generator๐Ÿ“ท OCR / Image to Textโฌ› Aspect Ratio CalculatorNumber of Digits CalculatorRoman Numerals ConverterMercury Retrograde CalendarAudio SplitterRandom IMEI GeneratorLog Base 10 CalculatorVertical Jump CalculatorSHA256 Hash GeneratorMP3 LooperRandom Superpower GeneratorBitwise CalculatorRandom Birthday GeneratorMerge VideosRandom Credit Card GeneratorOPS CalculatorCm to Feet and Inches ConverterRandom Activity GeneratorSquare Root (โˆš) CalculatorSaturn Return CalculatorSalary Conversion CalculatorCompound Growth CalculatorPhone Number ExtractorAI Text HumanizerWord Ladder GeneratorYouTube Channel StatisticsFile Size ConverterRandom Fake Address GeneratorCaffeine Overdose CalculatorRandom Meal GeneratorHalfway Date CalculatorMaster Number CalculatorRandom Poker Hand GeneratorOn Base Percentage CalculatorRandom Writing Prompt GeneratorSlugging Percentage CalculatorText FormatterWeight Loss CalculatorNumber to Word ConverterCompare Two StringsIP Subnet CalculatorBattery Life CalculatorStair CalculatorWAR CalculatorLottery Number GeneratorRandom Movie PickerBinary to Gray Code Converter๐Ÿ–ฑ๏ธ Click CounterRandom Group Generator๐Ÿ“… Date CalculatorDecimal to BCD ConverterQuotient and Remainder CalculatorPerfect Number CheckerRandom Time GeneratorAdd Text to ImageProportion CalculatorBCD to Decimal ConverterVideo to Image ExtractorRandom Loadout GeneratorLeap Years ListVideo CompressorSun Position CalculatorLove Compatibility CalculatorWord Scramble GeneratorImage SplitterDay of the Year Calculator - What Day of the Year Is It Today?SHA512 Hash GeneratorGray Code to Binary ConverterConnect the Dots GeneratorTime Duration CalculatorBreak Line by CharactersPercent Growth Rate CalculatorOctal CalculatorFirst n Digits of PiBingo Card GeneratorCM to Inches ConverterRandom User-Agent GeneratorYouTube Tag ExtractorRemove Lines Containing...List of Prime NumbersAcreage CalculatorArc Length CalculatorNumber ExtractorBcrypt Hash Generator / CheckerHebrew Calendar ConverterMartingale Strategy CalculatorRandom Emoji GeneratorSocial Media Username CheckerWHIP CalculatorAI Punctuation AdderModulo CalculatorBinary to BCD ConverterAstrological Element Balance CalculatorLong Division CalculatorBolt Torque CalculatorSmall Text Generator โฝแถœแต’แต–สธ โฟ แต–แตƒหขแต—แต‰โพRatio to Percentage CalculatorEmail ExtractorIP Address to Hex ConverterSteel Weight CalculatorWhat is my Lucky Number?API TesterWhat is my Zodiac Sign?Mandelbrot Set ExplorerBroken Link Checker๐ŸŽฐ Gacha Pity CalculatorFlip VideoAI Language DetectorPER Calculator๐Ÿ” Plagiarism CheckerRatio CalculatorCone Flat Pattern (Template) GeneratorRandom Number PickerMolarity CalculatorList RandomizerSort Lines AlphabeticallyImage CompressorHypotenuse CalculatorLunar Calendar ConverterPercentile CalculatorRandom Tournament Bracket Generator1099 Tax CalculatorAdjust Video SpeedSourdough CalculatorRemove Leading Trailing SpacesColor InverterDay of Year CalendarURL ExtractorHeight Percentile CalculatorVideo SplitterSum of Positive Integers CalculatorRandom Chess Opening GeneratorMD5 Hash GeneratorRandom Line PickerBoxing Punch Power CalculatorYouTube Comment PickerLinear Programming SolverMAC Address AnalyzerRemove AccentLaw of Sines CalculatorMultiple Fraction CalculatorRandomize NumbersHTML CompressorRemove Audio from VideoName Randomizer๐Ÿ”Š Tone GeneratorAI ParaphraserJob FinderShort Selling Profit CalculatorBirth Day of the Week CalculatorFence CalculatorRandom PIN GeneratorOutlier CalculatorLongest Day of the YearMiter Angle CalculatorRMD CalculatorSocial Media Post Time OptimizerPercentage Increase CalculatorAdd Prefix and Suffix to TextCollage MakerIncome Tax CalculatorRandom Math Problem GeneratorNumber Randomizer๐Ÿ’ง Dew Point CalculatorName Number CalculatorPVIFA CalculatorRandom Excuse GeneratorTessellation GeneratorTrigonometric Equation SolverCoin FlipperBeer Chill Time CalculatorCrossword Puzzle MakerYouTube Earnings EstimatorHex to BCD ConverterBCD to Binary ConverterBCD to Hex ConverterMedian CalculatorStandard Error CalculatorAverage CalculatorReverse VideoActual Cash Value CalculatorScientific Notation to Decimal ConverterAngel Number CalculatorLog Base 2 CalculatorRoot Mean Square CalculatorSHA3-256 Hash GeneratorAI Sentence ExpanderLbs to Kg ConverterHex to Decimal ConverterConvolution CalculatorRandom String GeneratorAmortization CalculatorMarkup CalculatorPVIF CalculatorDecimal to Hex ConverterInstagram Font GeneratorSocial Media Image Size GuideTikTok Money CalculatorTwitter/X Character CounterTwitter/X Timestamp ConverterYouTube Watch Time CalculatorTwitch Earnings CalculatorYouTube Shorts Monetization CalculatorFacebook Ad Cost CalculatorSocial Media ROI CalculatorCTR 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 CalculatorBoiling Point 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 Calculator