Prime Number Generator
Generate the first N prime numbers or list all primes inside a custom range. Includes prime count, largest prime, total sum, average prime gap, and twin-prime pair count for quick number-theory exploration.
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📐
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.
| Type | Formula | Best For |
|---|---|---|
| Arithmetic | Σxᵢ / n | Symmetric data, test scores, temperatures |
| Geometric | ⁿ√(x₁ × x₂ × … × xₙ) | Growth rates, investment returns, ratios |
| Harmonic | n / Σ(1/xᵢ) | Speeds, rates, frequencies |
| Quadratic | √(Σxᵢ² / n) | RMS — AC electricity, signal processing |
| Weighted | Σ(wᵢ·xᵢ) / Σwᵢ | Grades, portfolio returns, survey data |
| Trimmed | Arithmetic mean after trimming | Robust 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
- 1Choose a modeStandard: calculates all mean types from a flat list. Weighted: lets you assign a weight to each value, ideal for grade calculators and portfolio returns.
- 2Enter your numbersType 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.
- 3Add 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.
- 4Set 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.
- 5Read all six resultsAll 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.
| Subject | Grade | Credits (w) | Grade × Credits |
|---|---|---|---|
| Mathematics | 90 | 4 | 360 |
| English | 80 | 3 | 240 |
| PE | 95 | 1 | 95 |
| Weighted Mean | 695 ÷ 8 | 86.875 | |
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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Mean Calculator is part of the Math & Statistics Calculators collection. If you want a broader view of similar workflows, open the Math & Statistics Calculators category page or browse all QuickTools categories.
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