⚡ QuickTools
📐

Mean Calculator

Calculate all six types of mean simultaneously — Arithmetic, Geometric, Harmonic, Quadratic (RMS), Weighted, and Trimmed. Paste any dataset and instantly get the right average for your context, plus median, mode, standard deviation, variance, and coefficient of variation.

10 values parsed

Arithmetic Mean
79.6
Sum 796 ÷ 10 values
Geometric Mean
79.1248
Harmonic Mean
78.6402
Quadratic Mean (RMS)
80.0625
Median
80.5
Descriptive Statistics
Count
10
Min
65
Max
91
Range
26
Sum
796
Median
80.5
Pop StdDev
8.59302
Sample StdDev
9.05784
CV: 10.7953%Pop Variance: 73.84
Sorted values (10)
65697276788384889091

What Is the Mean?

In statistics, the mean is a measure of central tendency — a single value that represents the "centre" of a dataset. But "mean" is not one formula: there are five distinct types, each appropriate in different contexts. This calculator computes all of them simultaneously so you can choose the right one for your data.

TypeFormulaBest For
ArithmeticΣxᵢ / nSymmetric data, test scores, temperatures
Geometricⁿ√(x₁ × x₂ × … × xₙ)Growth rates, investment returns, ratios
Harmonicn / Σ(1/xᵢ)Speeds, rates, frequencies
Quadratic√(Σxᵢ² / n)RMS — AC electricity, signal processing
WeightedΣ(wᵢ·xᵢ) / ΣwᵢGrades, portfolio returns, survey data
TrimmedArithmetic mean after trimmingRobust estimate, removes outlier effect
Golden rule: Arithmetic Mean ≥ Geometric Mean ≥ Harmonic Mean for any set of positive numbers. They are equal only when all values are identical.

How to Use This Calculator

  1. 1
    Choose a mode
    Standard: calculates all mean types from a flat list. Weighted: lets you assign a weight to each value, ideal for grade calculators and portfolio returns.
  2. 2
    Enter your numbers
    Type or paste values separated by commas, spaces, or newlines. Try the quick-load sample datasets to see it in action. Up to 10,000 values supported.
  3. 3
    Add weights (optional)
    In Weighted mode, enter one weight per value in the same order. Weights can be any non-negative numbers — they don't need to sum to 1 or 100.
  4. 4
    Set trim % (optional)
    Use the trim slider to exclude extreme values. A 10% trim discards the bottom 10% and top 10% of values before computing the arithmetic mean.
  5. 5
    Read all six results
    All applicable means are displayed instantly alongside 8 descriptive statistics. Copy all results to clipboard with one click.

How Each Mean Is Calculated

📐

Arithmetic Mean

μ = (x₁ + x₂ + … + xₙ) / n

The classic average. Add all values, divide by count. Sensitive to outliers.

📈

Geometric Mean

GM = ⁿ√(x₁ · x₂ · … · xₙ)

Equivalent to the arithmetic mean of logarithms. Use for multiplicative processes. Requires all positive values.

Harmonic Mean

HM = n / (1/x₁ + 1/x₂ + … + 1/xₙ)

Reciprocal of the arithmetic mean of reciprocals. Ideal for speed, frequency, and rate problems.

🔌

Quadratic Mean (RMS)

QM = √( (x₁² + x₂² + … + xₙ²) / n )

Root mean square. Used in engineering for AC voltage/current and signal processing.

⚖️

Weighted Mean

WM = Σ(wᵢ · xᵢ) / Σwᵢ

Each value contributes proportionally to its weight. Higher weight = more influence on the result.

✂️

Trimmed Mean

Sort → remove p% from each end → arithmetic mean

Robust to outliers. A 20% trimmed mean is very close to the median for heavily skewed data.

Worked Examples

① Student Grade Calculator (Weighted Mean)

A student's grades are weighted by credit hours: Mathematics (A = 90) × 4 credits, English (B = 80) × 3 credits, PE (A = 95) × 1 credit.

SubjectGradeCredits (w)Grade × Credits
Mathematics904360
English803240
PE95195
Weighted Mean695 ÷ 886.875

Arithmetic mean = (90+80+95)/3 = 88.3 — but the weighted mean = 86.875 better reflects the course importance.

② Investment Return (Geometric Mean)

A fund returns +20%, −10%, +35% over three years. What is the average annual compound return?

Multipliers: 1.20 × 0.90 × 1.35 = 1.458
GM = ∛1.458 = 1.1336 → annual return = 13.36%
Arithmetic mean of percentages = (20 − 10 + 35)/3 = 15% — incorrectly higher

③ Average Speed (Harmonic Mean)

A car travels 100 km at 60 km/h, then 100 km at 40 km/h. What is the average speed?

HM = 2 / (1/60 + 1/40) = 2 / (0.0167 + 0.025) = 48 km/h
Arithmetic mean = (60+40)/2 = 50 km/h — overestimates actual average speed

④ Outlier-Resistant Mean (Trimmed)

A dataset of house prices: $200K, $210K, $215K, $220K, $225K, $230K, $1.5M (outlier). The 10% trimmed mean removes the extreme values and gives a more representative estimate.

Arithmetic Mean
$400,000
inflated by outlier
Trimmed Mean (14%)
$220,000
representative estimate

Frequently Asked Questions

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