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

Average Calculator

Calculate mean, median, mode, geometric mean, harmonic mean, and weighted average with complete statistical analysis, visualizations, and step-by-step solutions.

Average Calculator

Try these examples:

Simple Set Test Scores Growth Rates Weighted GPA Large Dataset
Separate numbers with commas, spaces, or line breaks. Supports up to 10,000 numbers.
Enter weights matching each value for weighted average calculation.

Embed Average Calculator Widget

About Average Calculator

The Average Calculator is a comprehensive statistical tool that calculates the mean (average), median, mode, geometric mean, harmonic mean, and weighted average of any dataset. It provides complete statistical analysis including variance, standard deviation, range, and interactive visualizations with step-by-step calculation breakdowns. Whether you are a student, researcher, data analyst, or professional, this calculator handles datasets up to 10,000 numbers with adjustable precision.

What is an Average (Mean)?

The arithmetic mean, commonly called the average, is the sum of all values divided by the count of values. It represents the central tendency of a dataset and is the most widely used measure of average in statistics, everyday life, and scientific research.

Arithmetic Mean Formula
Mean = (x₁ + x₂ + ... + xₙ) / n

For example, the average of 10, 20, 30, 40, and 50 is (10+20+30+40+50)/5 = 150/5 = 30.

Types of Averages Explained

Arithmetic Mean

The standard average calculated by summing all values and dividing by the count. Best used for datasets without extreme outliers and when values are measured on an interval or ratio scale (like temperatures, heights, or test scores).

Median

The middle value when data is sorted in order. For an odd number of values, it is the exact middle value. For an even number, it is the average of the two middle values. The median is resistant to outliers, making it ideal for skewed distributions like income or housing prices.

Median
For n values: Middle value if n is odd, or Average of two middle values if n is even

Mode

The most frequently occurring value(s) in a dataset. A dataset can have no mode (all values appear once), one mode (unimodal), two modes (bimodal), or multiple modes (multimodal). Mode is particularly useful for categorical data or finding the most common value.

Geometric Mean

The nth root of the product of n values. Used for averaging growth rates, percentages, ratios, or when data spans multiple orders of magnitude. Only defined for positive numbers.

Geometric Mean Formula
GM = ⁿ√(x₁ × x₂ × ... × xₙ)

Example: Investment returns of 10%, 20%, and -5% (as multipliers: 1.10, 1.20, 0.95). Geometric mean = (1.10 × 1.20 × 0.95)^(1/3) = 1.0747, indicating 7.47% average annual return.

Harmonic Mean

The reciprocal of the arithmetic mean of reciprocals. Best for averaging rates when the quantity in the denominator varies, such as speeds over equal distances or prices when buying equal dollar amounts.

Harmonic Mean Formula
HM = n / (1/x₁ + 1/x₂ + ... + 1/xₙ)

Example: Driving 60 mph to a destination and 40 mph back. Harmonic mean = 2/(1/60 + 1/40) = 48 mph, which is the correct average speed for the round trip.

Weighted Average

An average where each value is multiplied by a weight representing its relative importance. Used in GPA calculations, financial portfolios, and any situation where values have different significance.

Weighted Average Formula
Weighted Average = (w₁x₁ + w₂x₂ + ... + wₙxₙ) / (w₁ + w₂ + ... + wₙ)

Statistical Measures Provided

Variance

Variance measures how spread out values are from the mean. Population variance divides by n and is used when you have data for the entire population. Sample variance divides by n-1 (Bessel's correction) and provides an unbiased estimate when working with a sample from a larger population.

Variance Formula
Population: σ² = Σ(xᵢ - μ)² / n   |   Sample: s² = Σ(xᵢ - x̄)² / (n-1)

Standard Deviation

The square root of variance, expressed in the same units as the original data. It indicates the typical distance of values from the mean. About 68% of data falls within one standard deviation of the mean in a normal distribution, and about 95% within two standard deviations.

Range

The difference between the maximum and minimum values. Range = Maximum - Minimum. A simple measure of spread, though sensitive to outliers.

How to Use This Calculator

  1. Enter your data: Input numbers separated by commas, spaces, or line breaks. You can paste data directly from spreadsheets or text files.
  2. Add weights (optional): For weighted average calculations, enter corresponding weights in the weights field. Each weight should match its value in order.
  3. Select decimal precision: Choose how many decimal places you want in the results, from 0 (whole numbers) to 20 places for high precision calculations.
  4. Click Calculate: View comprehensive results including all types of averages, variance, standard deviation, interactive charts, and step-by-step calculations.

When to Use Different Types of Averages

Use Arithmetic Mean When:

Use Median When:

Use Mode When:

Use Geometric Mean When:

Use Harmonic Mean When:

Practical Examples

Example 1: Class Test Scores

A class of 10 students scored: 78, 85, 92, 88, 76, 95, 82, 79, 88, 91

Example 2: Investment Returns

Annual returns over 3 years: +15%, -10%, +25% (as multipliers: 1.15, 0.90, 1.25)

Example 3: GPA Calculation (Weighted Average)

Grades: A (4.0), B (3.0), A (4.0), C (2.0) with credits: 3, 4, 3, 2

Frequently Asked Questions

What is the difference between mean, median, and mode?

Mean is the arithmetic average calculated by summing all values and dividing by the count. Median is the middle value when data is sorted; for even-count datasets, it is the average of two middle values. Mode is the most frequently occurring value(s). Each measure serves different purposes: mean for typical values in symmetric distributions, median for skewed data or when outliers exist, and mode for categorical data or finding the most common value.

When should I use geometric mean vs arithmetic mean?

Use geometric mean when averaging growth rates, percentages, ratios, or when data spans multiple orders of magnitude. For example, investment returns over multiple years should use geometric mean. Arithmetic mean is appropriate for adding absolute values like heights, weights, or test scores. Geometric mean always equals or is less than arithmetic mean.

What is harmonic mean used for?

Harmonic mean is ideal for averaging rates, such as speeds over equal distances, prices when buying equal dollar amounts, or any situation involving ratios with constant numerators. For example, if you drive 60 mph for one trip and 40 mph on the return, the harmonic mean (48 mph) correctly represents your average speed, not the arithmetic mean (50 mph).

How do I calculate weighted average?

Weighted average multiplies each value by its weight, sums these products, then divides by the sum of weights. Formula: Weighted Average = (w1*x1 + w2*x2 + ... + wn*xn) / (w1 + w2 + ... + wn). Use this calculator by entering values in the first field and corresponding weights in the optional weights field.

What is the difference between population and sample standard deviation?

Population standard deviation (divides by n) is used when your data represents the entire population. Sample standard deviation (divides by n-1, known as Bessel's correction) is used when data is a sample from a larger population, providing an unbiased estimate. For most real-world applications, sample standard deviation is appropriate.

Why does geometric mean only work with positive numbers?

Geometric mean involves multiplying all values and taking the nth root. Negative numbers or zero would create undefined or misleading results (negative products with odd counts, zero products, complex numbers with even counts of negatives). For growth rates that include negative values, convert to multipliers first (e.g., -10% becomes 0.90).

How many numbers can this calculator handle?

This calculator efficiently processes up to 10,000 numbers. For larger datasets, consider using specialized statistical software. The calculator provides instant results for typical educational and professional use cases.

Related Statistical Tools

Reference this content, page, or tool as:

"Average Calculator" at https://MiniWebtool.com/average-calculator/ from MiniWebtool, https://MiniWebtool.com/

by miniwebtool team. Updated: Jan 06, 2026

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

Related MiniWebtools:

Sum CalculatorFeatured

Statistics And Data Analysis:

Top & Updated:

Random PickerRandom Name PickerRelative Standard Deviation CalculatorMAC Address GeneratorMAC Address LookupFPS ConverterSort NumbersFeet and Inches to Cm ConverterRemove SpacesRandom Quote GeneratorWord to Phone Number ConverterLine CounterSum CalculatorPercent Off CalculatorBitwise CalculatorNumber of Digits CalculatorBatting Average CalculatorRoman Numerals ConverterSHA256 Hash GeneratorSalary Conversion CalculatorFacebook User ID LookupLog Base 10 CalculatorSquare Root (√) CalculatorSaturn Return CalculatorAI Punctuation AdderERA CalculatorPhone Number ExtractorVideo to Image ExtractorBinary to Gray Code ConverterDecimal to BCD ConverterCm to Feet and Inches ConverterSun, Moon & Rising Sign Calculator 🌞🌙✨Remove AccentMP3 LooperCompound Growth CalculatorBCD to Decimal ConverterRemove Audio from VideoPercent Growth Rate CalculatorRemove Lines Containing...Quotient and Remainder CalculatorAI ParaphraserFirst n Digits of PiDay of Year CalendarText FormatterPercentage Increase CalculatorMaster Number CalculatorTime Duration CalculatorLove Compatibility CalculatorGray Code to Binary ConverterRandom Birthday GeneratorModulo CalculatorOutlier CalculatorProportion CalculatorCompare Two StringsMerge VideosBinary to BCD ConverterInvisible Text Generator📅 Date CalculatorASCII Art GeneratorList of Prime NumbersLeap Years ListMultiplication CalculatorAdd or Replace Audio in VideoIP Address to Hex ConverterNumber to Word ConverterAudio SplitterRandom Group GeneratorScientific Notation to Decimal ConverterVideo CompressorHypotenuse CalculatorAdd Prefix and Suffix to TextRatio to Percentage CalculatorPER CalculatorRandom Number PickerSlugging Percentage CalculatorNumber ExtractorExponents CalculatorHex to BCD ConverterMedian CalculatorDay of the Year Calculator - What Day of the Year Is It Today?Name Number CalculatorSHA512 Hash GeneratorOn Base Percentage CalculatorNatural Log CalculatorBCD to Binary ConverterFraction CalculatorAverage Deviation CalculatorAmortization CalculatorBreak Line by CharactersPythagorean Theorem CalculatorOctal ConverterLog Base 2 CalculatorRemove Leading Trailing SpacesLife Path Number CalculatorVideo SplitterAdjust Video SpeedInvisible Character RemoverActual Cash Value CalculatorBonus CalculatorVideo CropperOctal CalculatorEmail ExtractorURL ExtractorOPS CalculatorWHIP CalculatorSort Lines AlphabeticallyLottery Number GeneratorBCD to Hex ConverterStandard Error CalculatorList RandomizerAverage CalculatorPVIFA CalculatorReverse VideoWAR CalculatorAngel Number CalculatorRoot Mean Square CalculatorSum of Positive Integers CalculatorSHA3-256 Hash GeneratorAI Sentence ExpanderLbs to Kg ConverterHex to Decimal ConverterConvolution CalculatorMAC Address AnalyzerRandom String GeneratorMarkup CalculatorPVIF CalculatorDecimal to Hex ConverterList of Fibonacci NumbersBlood Donation Time CalculatorAntilog CalculatorField Goal Percentage CalculatorRandom Line PickerAPY to APR CalculatorSort Text By LengthRandom Object GeneratorOne Rep Max (1RM) CalculatorName RandomizerRandom Animal GeneratorSquare Numbers ListFixed Deposit CalculatorPPM to Percent ConverterCube Numbers ListCaesar Cipher ToolMorse Code GeneratorPercent to PPM ConverterSRT to TXT Converterkg to lbs ConverterXML ValidatorArithmetic Mean CalculatorJob FinderCAGR CalculatorStatistics CalculatorSRT Time ShiftFirst n Digits of eFVIFA Calculator (High Precision)Exponential Integral CalculatorLoop VideoMD5 Hash GeneratorSHA1 Hash GeneratorRandom Name GeneratorIs it a Prime Number?Binary CalculatorDiscount Factor CalculatorDecimal to Binary ConverterExponential Decay CalculatorStandard Deviation CalculatorMaze GeneratorDoubling Time CalculatorBarcode GeneratorWork Hours CalculatorCM to Inches ConverterAudio ExtractorExponential Growth Calculator (High Precision)Quote FinderHEX CalculatorPopulation Standard Deviation CalculatorRandom Word GeneratorAdd Watermark to VideoRotate VideoFlip VideoFlip GIFFlip ImageInches to cm ConverterIP Address to Binary ConverterReduce Fractions CalculatorGIF to MP4 ConverterMP4 to GIF ConverterColor InverterAdd Text to ImageImage EnhancerImage SplitterImage Color PickerAdd Line to ImagePalette GeneratorpH CalculatorMolar Mass CalculatorReverse LineMolarity CalculatorAngle ConverterWeight (Mass) ConverterLength ConverterVolume ConverterPressure ConverterEnergy ConverterShoe Size ConverterSpeed ConverterTemperature ConverterPower ConverterImage RotatorHousing Appreciation CalculatorCar Depreciation CalculatorHome Affordability CalculatorDestiny Number CalculatorMortgage Comparison CalculatorCompound Savings CalculatorIRR CalculatorImage CensorImage CompressorFuture Value Factor (FVIF) CalculatorUltimate Frequency & Wavelength Convertern-th Root Calculator (High-Precision)Cron Job GeneratorUnix Permission Calculator (chmod)Venus Sign Calculator (Love Style) 💖Mars Sign Calculator (Drive & Passion) 🔥Password Strength TesterMercury Sign CalculatorAstrological Element Balance CalculatorAstrological Modality Balance CalculatorMercury Retrograde Calendar 🌟New Moon & Full Moon CalendarAdvanced Zodiac Compatibility Analyzer 💞Moon Sign Compatibility Calculator 🌙Celtic Tree Zodiac Calculator 🌳Birthstone and Zodiac Flower Finder 💎🌸Concrete Calculator 🧱Brick and Mortar Calculator 🧱Paint Calculator 🎨Tile Calculator 🔲Flooring Calculator 🏠Drywall Calculator 🧱Wallpaper Calculator 🎨Stair Calculator 🪜Roof Pitch and Rafter Calculator 🏠Roofing Calculator 🏠Stud Wall Framing Calculator 🏗️Mulch, Soil, and Gravel Calculator 🌱Fence Calculator 🏡Decking Calculator 🏗️Board Foot Calculator 🪵Squareness Checker (3-4-5 Rule) 📐Miter Angle Calculator 📐Slope and Grade Calculator 📐Sine CalculatorCosine CalculatorHigh-Precision Tangent CalculatorArcsin CalculatorArccos (Inverse Cosine) CalculatorArctan CalculatorArctan2 CalculatorCosecant/Secant/Cotangent CalculatorHyperbolic Functions CalculatorRight Triangle CalculatorGeneral Triangle SolverLaw of Sines CalculatorLaw of Cosines CalculatorDMS to Decimal Degrees ConverterDecimal Degrees to DMS ConverterHigh-Precision Polar to Cartesian Coordinates ConverterHigh-Precision Cartesian to Polar Coordinates ConverterInteractive Unit Circle VisualizerTrigonometric Identities CalculatorTrigonometric Function GrapherAlgebraic Expression SimplifierRadical SimplifierRational Expression CalculatorPolynomial Factoring CalculatorExpand Polynomials CalculatorPolynomial Long Division CalculatorSynthetic Division CalculatorLinear Equation SolverAbsolute Value Equation SolverRadical Equation SolverSystem of Linear Equations SolverInequality SolverAbsolute Value Inequality SolverSystem of Inequalities GrapherFunction GrapherDomain and Range CalculatorInverse Function CalculatorFunction Composition CalculatorVertex and Axis of Symmetry CalculatorX and Y Intercept CalculatorHTML Entity Encoder/DecoderURL Slug GeneratorJSON String Escape/UnescapeMarkdown Table GeneratorSmart Quotes RemoverDaily Time Savings CalculatorLorem Ipsum GeneratorReadability Score CalculatorKeyword Density CheckerBionic Reading ConverterText to Speech ReaderFancy Text GeneratorZalgo Text GeneratorUpside Down Text GeneratorList Difference CalculatorText Column ExtractorText to SQL List ConverterStock 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 Calculator