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

Quartile Deviation Calculator

Calculate the quartile deviation (semi-interquartile range) of a dataset with interactive box plot visualization, complete quartile analysis (Q1, Q2, Q3, IQR), outlier detection, and step-by-step calculation breakdown.

Quartile Deviation Calculator

Try these example datasets:

Simple Set Test Scores With Outlier Decimals

Separate numbers with comma, space, or line break. If your text has non-numeric content, use our Number Extractor first.

Embed Quartile Deviation Calculator Widget

About Quartile Deviation Calculator

The Quartile Deviation Calculator is a comprehensive statistical tool that calculates the quartile deviation (also known as the semi-interquartile range) of your dataset. This calculator provides a complete five-number summary, interactive box plot visualization, automatic outlier detection using the 1.5 IQR rule, and detailed step-by-step calculation breakdowns. Whether you are a student learning statistics, a researcher analyzing data, or a professional making data-driven decisions, this tool helps you understand the spread and distribution of your data.

What is Quartile Deviation?

Quartile deviation (QD), also called the semi-interquartile range (SIQR), is a measure of statistical dispersion that indicates how spread out the middle 50% of your data is. It is calculated as half the interquartile range (IQR):

Quartile Deviation Formula
$$QD = \frac{Q_3 - Q_1}{2} = \frac{IQR}{2}$$

Where:

Why Use Quartile Deviation?

Understanding Quartiles and IQR

The Three Quartiles

Quartiles divide a sorted dataset into four equal parts:

Interquartile Range (IQR)

The interquartile range is the difference between Q3 and Q1, representing the range of the middle 50% of data. It is a key measure of spread that forms the basis for quartile deviation and outlier detection.

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

The relationship between IQR and quartile deviation is simple: QD = IQR / 2. This means the quartile deviation represents the average spread from the median to each quartile boundary.

How to Use This Calculator

  1. Enter your data: Input numbers in the text area, separated by commas, spaces, or line breaks. The calculator accepts both integers and decimals, including negative numbers.
  2. Use example data (optional): Click any example button to load pre-set datasets demonstrating different scenarios like normal distributions, datasets with outliers, or test scores.
  3. Click Calculate: Press the "Calculate Quartile Deviation" button to process your data.
  4. Review the quartile summary: Examine Q1, Q2 (median), Q3, IQR, and the quartile deviation prominently displayed.
  5. Analyze the box plot: The interactive box plot visualizes your data distribution, showing quartiles, whiskers, and outliers.
  6. Check for outliers: The calculator automatically detects outliers using the 1.5 IQR rule.
  7. Study the step-by-step breakdown: Expand the detailed calculation section to understand exactly how each value was computed.

The Five-Number Summary

The five-number summary provides a complete picture of your data distribution:

Statistic Description Percentile
Minimum Smallest value in the dataset 0th
Q1 (First Quartile) Median of lower half 25th
Q2 (Median) Middle value 50th
Q3 (Third Quartile) Median of upper half 75th
Maximum Largest value in the dataset 100th

Outlier Detection with IQR

This calculator uses the 1.5 IQR rule (Tukey's method) to detect outliers:

The calculator distinguishes between:

Quartile Deviation vs Standard Deviation

Aspect Quartile Deviation Standard Deviation
Calculation basis Uses Q1 and Q3 only Uses all data points
Outlier sensitivity Robust (not affected) Sensitive (heavily affected)
Best for Skewed or ordinal data Normal distributions
Interpretation Average distance to quartiles Average distance to mean
Normal distribution relationship QD approximately equals 0.67 times SD SD approximately equals 1.5 times QD

Coefficient of Quartile Deviation

The coefficient of quartile deviation (CQD) is a relative measure of dispersion that allows comparison between datasets with different units or scales:

Coefficient of Quartile Deviation
$$CQD = \frac{Q_3 - Q_1}{Q_3 + Q_1} \times 100\%$$

The CQD is useful when comparing variability across datasets with different means or units. A higher CQD indicates greater relative dispersion.

Real-World Applications

Education and Testing

Quartile deviation helps educators understand score distributions. A small QD indicates students performed similarly, while a large QD suggests wide variation in performance.

Quality Control

Manufacturing uses quartile deviation to assess product consistency. Products with low QD have more uniform specifications.

Finance and Economics

Financial analysts use QD to measure income inequality, price stability, and investment risk in ways that are not skewed by extreme values.

Healthcare

Medical researchers use quartile-based statistics to analyze patient data, treatment outcomes, and biological measurements that may not be normally distributed.

Social Sciences

Survey data often has ordinal scales where quartile deviation is more appropriate than standard deviation for measuring spread.

Step-by-Step Calculation Example

For the dataset: 2, 4, 6, 8, 10, 12, 14, 16, 18

  1. Sort the data: 2, 4, 6, 8, 10, 12, 14, 16, 18 (n = 9)
  2. Find Q2 (Median): Middle value = x5 = 10
  3. Find Q1: Median of lower half (2, 4, 6, 8) = (4 + 6) / 2 = 5
  4. Find Q3: Median of upper half (12, 14, 16, 18) = (14 + 16) / 2 = 15
  5. Calculate IQR: 15 - 5 = 10
  6. Calculate QD: 10 / 2 = 5

The quartile deviation of 5 means that on average, values in the middle 50% of the data are within 5 units of the median.

Frequently Asked Questions

What is quartile deviation?

Quartile deviation (QD), also known as semi-interquartile range (SIQR), is a measure of statistical dispersion equal to half the interquartile range (IQR). It is calculated as QD = (Q3 - Q1) / 2, where Q3 is the third quartile (75th percentile) and Q1 is the first quartile (25th percentile). Quartile deviation measures the spread of the middle 50% of data and is robust to outliers.

How do you calculate quartile deviation step by step?

To calculate quartile deviation: 1) Sort your data in ascending order. 2) Find Q1 (first quartile) - the median of the lower half of data. 3) Find Q3 (third quartile) - the median of the upper half of data. 4) Calculate IQR = Q3 - Q1. 5) Calculate QD = IQR / 2. For example, with data 2, 4, 6, 8, 10, 12, 14: Q1 = 4, Q3 = 12, IQR = 8, QD = 4.

What is the difference between quartile deviation and standard deviation?

Quartile deviation and standard deviation both measure data spread, but differ in key ways. Quartile deviation uses quartiles (Q1 and Q3) and is robust to outliers, making it ideal for skewed data. Standard deviation uses all data points and squares the differences from the mean, making it sensitive to outliers. For normally distributed data, standard deviation is approximately 1.5 times the quartile deviation.

What is the interquartile range (IQR)?

The interquartile range (IQR) is the difference between the third quartile (Q3) and first quartile (Q1), representing the range of the middle 50% of data. IQR = Q3 - Q1. The IQR is twice the quartile deviation. It is commonly used for outlier detection: values below Q1 - 1.5 times IQR or above Q3 + 1.5 times IQR are considered potential outliers.

What is the coefficient of quartile deviation?

The coefficient of quartile deviation (CQD), also called the quartile coefficient of dispersion, is a relative measure of variability that allows comparison between datasets with different units or scales. It is calculated as CQD = (Q3 - Q1) / (Q3 + Q1) times 100. The result is expressed as a percentage, with higher values indicating greater relative dispersion.

Additional Resources

To learn more about quartile deviation and statistical measures of dispersion:

Reference this content, page, or tool as:

"Quartile Deviation Calculator" at https://MiniWebtool.com/quartile-deviation-calculator/ from MiniWebtool, https://MiniWebtool.com/

by miniwebtool team. Updated: Jan 05, 2026

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

Related MiniWebtools:

Quartile Calculator

Statistics And Data Analysis:

Top & Updated:

Random PickerRandom Name PickerRelative Standard Deviation CalculatorLine CounterSort NumbersFPS ConverterMAC Address GeneratorMAC Address LookupBatting Average CalculatorRemove SpacesFeet and Inches to Cm ConverterERA CalculatorWord to Phone Number ConverterRandom Truth or Dare GeneratorPercent Off CalculatorRandom Quote GeneratorSum CalculatorFacebook User ID LookupSaturn Return CalculatorLog Base 10 CalculatorBitwise CalculatorText FormatterSHA256 Hash GeneratorNumber of Digits CalculatorCm to Feet and Inches ConverterRoman Numerals ConverterPhone Number ExtractorAI ParaphraserOn Base Percentage CalculatorSun, Moon & Rising Sign Calculator 🌞🌙✨Instagram User ID LookupVideo to Image ExtractorSquare Root (√) CalculatorSlugging Percentage CalculatorSalary Conversion CalculatorOutlier CalculatorCompound Growth CalculatorFirst n Digits of PiQuotient and Remainder CalculatorBinary to Gray Code ConverterMP3 LooperNumber to Word ConverterOctal CalculatorAI Punctuation AdderOPS CalculatorRandom Superpower GeneratorAntilog CalculatorPER CalculatorBCD to Decimal ConverterStandard Error CalculatorRandom Birthday GeneratorDay of Year CalendarAudio SplitterLeap Years ListDecimal to BCD ConverterRemove AccentRemove Audio from VideoMerge VideosTime Duration CalculatorLove Compatibility CalculatorLog Base 2 CalculatorRandom Credit Card GeneratorMedian CalculatorBase-N CalculatorScientific Notation to Decimal ConverterName Number CalculatorIP Address to Hex ConverterRandom Movie PickerPercent Growth Rate CalculatorMultiplication CalculatorRandom Group GeneratorCM to Inches ConverterGray Code to Binary ConverterNext Leap Year CalculatorDay of the Year Calculator - What Day of the Year Is It Today?SHA512 Hash GeneratorRemove Lines Containing...Bonus CalculatorAverage Deviation CalculatorList RandomizerField Goal Percentage CalculatorNumber ExtractorFirst n Digits of eRandom Emoji GeneratorBinary to BCD ConverterList of Prime NumbersModulo CalculatorCompare Two StringsVideo CompressorRatio to Percentage CalculatorMAC Address AnalyzerProportion CalculatorMaster Number CalculatorExponential Decay CalculatorRandom IMEI GeneratorVideo CropperRandom Tournament Bracket GeneratorComplex Number CalculatorPVIFA CalculatorInvisible Text GeneratorEmail ExtractorURL ExtractorAdd Prefix and Suffix to TextWHIP CalculatorSort Lines AlphabeticallyHex to BCD ConverterBCD to Binary ConverterLottery Number GeneratorBCD to Hex ConverterBreak Line by CharactersAverage CalculatorReverse VideoWAR CalculatorHypotenuse CalculatorActual Cash Value CalculatorAngel Number CalculatorRoot Mean Square CalculatorSum of Positive Integers CalculatorSHA3-256 Hash GeneratorAI Sentence Expander📅 Date CalculatorLbs to Kg ConverterHex to Decimal ConverterConvolution CalculatorRandom String GeneratorRemove Leading Trailing SpacesAmortization CalculatorMarkup CalculatorPVIF CalculatorDecimal to Hex ConverterDaily Time Savings CalculatorLorem Ipsum GeneratorReadability Score CalculatorKeyword Density CheckerBionic Reading ConverterText to Speech ReaderFancy Text GeneratorZalgo Text GeneratorUpside Down Text GeneratorASCII Art GeneratorList Difference CalculatorText Column ExtractorText to SQL List ConverterInvisible Character RemoverStock Average CalculatorPosition Size CalculatorMargin Call CalculatorShort Selling Profit CalculatorRisk of Ruin CalculatorBlack-Scholes Option Pricing CalculatorOption Greeks CalculatorImplied Volatility CalculatorOptions Profit CalculatorImpermanent Loss CalculatorCrypto Arbitrage CalculatorSatoshi to USD ConverterCrypto Leverage CalculatorPivot Point CalculatorFibonacci Extension CalculatorStop Loss & Take Profit CalculatorKelly Criterion CalculatorMartingale Strategy CalculatorCompound Daily Interest CalculatorPip Value CalculatorGaussian Distribution GeneratorRandom Meal GeneratorRandom Color Palette GeneratorRandom Country GeneratorRandom JSON GeneratorRandom User-Agent GeneratorRandom Coordinate GeneratorRandom Date GeneratorRandom Time GeneratorRandom IP Address GeneratorRandom Playing Card GeneratorMagic 8-BallRock Paper Scissors GeneratorCoin FlipperDice RollerSpin the WheelAquarium Volume & Stocking CalculatorAquarium Substrate CalculatorScale Model Conversion CalculatorPlant Spacing CalculatorDice Roll Probability CalculatorDepth of Field (DoF) CalculatorGolden Hour / Blue Hour CalculatorPrint Size & Resolution Calculator (DPI/PPI)Soap Making Lye Calculator (SAP)Candle Wax & Fragrance Oil CalculatorHomebrew ABV Calculator (Alcohol by Volume)Coffee Brew Ratio CalculatorBrine and Salinity CalculatorYarn CalculatorFabric CalculatorCross-Stitch Size CalculatorBaker's Percentage CalculatorDough Hydration CalculatorBaking Pan Size ConverterYeast Conversion CalculatorJSON to YAML ConverterJWT DecodercURL to JSON ConverterSQL FormatterCrontab Expression GeneratorFavicon GeneratorSVG OptimizerHtaccess Redirect GeneratorResistor Color Code CalculatorOhm's Law CalculatorVoltage Drop CalculatorPCB Trace Width CalculatorBattery Life CalculatorRandom PIN GeneratorRandom NanoID GeneratorRandom Port Number GeneratorRandom Fake Address GeneratorRandom User Persona GeneratorRandom Writing Prompt GeneratorRandom Haiku GeneratorRandom Domain Name GeneratorRandom Cocktail Recipe GeneratorRandom Activity GeneratorRandom Excuse GeneratorRandom US State GeneratorLemonade Stand CalculatorPizza Value CalculatorVampire Apocalypse CalculatorChristmas Tree CalculatorParking Ratio CalculatorGooglebot Crawl Size CheckerZombie Survival Time CalculatorHelium Balloon Lift CalculatorKinetic Energy Chicken CookerTeleportation Error Rate CalculatorHamster Power CalculatorBanana Radiation CalculatorFalling Through Earth CalculatorPenny Drop Impact CalculatorPopcorn Fill Room CalculatorLego Brick House CalculatorWedding Alcohol CalculatorPizza Party PlannerCaffeine Overdose CalculatorBBQ CalculatorTaco Bar CalculatorBeer Chill Time CalculatorSpaghetti Portion CalculatorCocktail ABV CalculatorChocolate Fountain CalculatorCheese Board CalculatorSudoku Generator & Solver24 Game Solver & TrainerNonogram Generator (Picross)KenKen Generator (Calcudoku)Kakuro GeneratorPoop Salary CalculatorMeeting Cost TickerCommute Life Wasted CalculatorFIRE CalculatorEmail Reply Time CalculatorCoffee vs. Sleep CalculatorReal Hourly Wage CalculatorSick Day Probability CalculatorBuzzword Bingo GeneratorKeyboard Mileage CalculatorToilet Paper Value CalculatorElectricity Cost of Bitcoin Mining CalculatorShower Cost CalculatorLight Bulb Savings CalculatorCat Calorie CalculatorHuman to Ant Weight ConverterTruth Table GeneratorSet Theory CalculatorVenn Diagram Generator (3 Sets)Chinese Remainder Theorem CalculatorEuler's Totient Function CalculatorExtended Euclidean Algorithm CalculatorModular Multiplicative Inverse CalculatorContinued Fraction CalculatorShoelace Formula CalculatorTriangle Centroid CalculatorTriangle Orthocenter CalculatorPoint to Plane Distance CalculatorSphere Equation CalculatorGram-Schmidt CalculatorVector Projection CalculatorMatrix LU Decomposition CalculatorRadius of Convergence CalculatorCurvature CalculatorCollatz Conjecture CalculatorHappy Number CalculatorMagic Square GeneratorDijkstra's Shortest Path CalculatorMinimum Spanning Tree CalculatorGraph Degree Sequence ValidatorCatalan Number GeneratorDerangement (Subfactorial) CalculatorStirling Numbers CalculatorPigeonhole Principle CalculatorMarkov Chain Steady State CalculatorGini Coefficient CalculatorSingular Value Decomposition (SVD) CalculatorRandom RPG Character GeneratorRandom Chess Opening GeneratorRandom Poker Hand GeneratorRandom Loadout GeneratorRandom Chord GeneratorRandom Sound Frequency GeneratorMatrix Rank CalculatorMatrix Trace CalculatorWronskian CalculatorRunge-Kutta (RK4) Method CalculatorFourier Series Coefficients CalculatorFunction Odd Even Neither CheckerCone Flat Pattern (Template) GeneratorPolygon Diagonals CalculatorEuler Characteristic CalculatorRSA Encryption Step-by-Step SimulatorPrimitive Root Calculator