Mean Median Mode Calculator
Free mean median mode calculator. Arithmetic, geometric, harmonic, trimmed, weighted mean. Median, m
Why This Statistical Analysis Matters
Why: Statistical calculator for analysis.
How: Enter inputs and compute results.
Mean, Median, Mode — All Central Tendency Measures
Arithmetic, geometric, harmonic, trimmed, weighted mean. Median, mode (unimodal/bimodal/multimodal). Skewness indicator. Step-by-step breakdown.
Real-World Scenarios — Click to Load
Data Input
Central Tendency Comparison
Histogram
Running Mean vs Running Median
Calculation Breakdown
⚠️For educational and informational purposes only. Verify with a qualified professional.
Key Takeaways
- • Mean: Σxᵢ/n — sensitive to outliers; use for symmetric data
- • Median: Middle value — robust; use for skewed data
- • Mode: Most frequent — unimodal, bimodal, or multimodal
- • Skewness: mean > median > mode → right-skewed; mean < median < mode → left-skewed
- • Trimmed mean: Removes k% from each tail — compromise between mean and median
- • Geometric mean: (∏xᵢ)^(1/n) — for growth rates, ratios
- • Harmonic mean: n/Σ(1/xᵢ) — for rates (e.g., average speed)
- • Weighted mean: Σ(wᵢxᵢ)/Σwᵢ — when values have different importance
Did You Know?
How Central Tendency Works
Mean = Σxᵢ/n
Sum all values, divide by count. The "average" in everyday use.
Median = Middle Value
Sort data; median is the middle (or average of two middle values). 50th percentile.
Mode = Most Frequent
Value(s) that appear most often. Unimodal (1), bimodal (2), or multimodal (3+).
Trimmed Mean
Remove k% from each tail, then average the rest. Reduces outlier impact.
Geometric vs Harmonic Mean
Geometric: (∏xᵢ)^(1/n) for growth. Harmonic: n/Σ(1/xᵢ) for rates.
Skewness and Central Tendency
| Distribution | Relationship |
|---|---|
| Symmetric | mean = median = mode |
| Right-skewed | mean > median > mode |
| Left-skewed | mean < median < mode |
Expert Tips
When to Use Each
Mean for symmetric data. Median for skewed or with outliers. Mode for categorical or discrete data with clear peaks.
Report Both Mean and Median
If they differ significantly, data is skewed. Reporting both gives a complete picture.
Frequently Asked Questions
When to use mean vs median?
Use mean for symmetric data without outliers. Use median for skewed data (income, house prices) or when outliers are present.
What is bimodal?
Bimodal means two values tie for the highest frequency. Common in mixed populations (e.g., heights of men and women combined).
What is the trimmed mean?
Trimmed mean removes a percentage from each tail (e.g., 10% top and 10% bottom) then averages the rest. Used in Olympic scoring.
When to use geometric mean?
For growth rates, ratios, or when values are multiplicative. Average of 2% and 8% growth is geometric: √(1.02×1.08)−1 ≈ 4.98%, not 5%.
When to use harmonic mean?
For rates (speed, density). If you drive 60 mph for 30 miles and 40 mph for 30 miles, average speed = 48 mph (harmonic of 60 and 40).
How to enter weighted data?
Use value,weight per line. Example: 3.5, 4 for grade 3.5 with 4 credit hours. The calculator computes weighted mean.
Formulas Reference
Mean = Σxᵢ / n
Arithmetic mean
Geometric mean = (∏xᵢ)^(1/n)
For positive values only
Harmonic mean = n / Σ(1/xᵢ)
For positive non-zero values
Weighted mean = Σ(wᵢxᵢ) / Σwᵢ
When weights differ
Central Tendency by the Numbers
Applications
Education
GPA (weighted mean), test scores (mean/median), grade distributions (mode).
Finance
Average returns (geometric mean), portfolio weights (weighted mean).
Demographics
Income (median for skewness), house prices, age distributions.
Scientific Research
Report mean ± SD for symmetric data; median (IQR) for skewed. Trimmed mean for robustness.
Official Data Sources
Disclaimer: Choose the appropriate measure for your data. Mean for symmetric data; median for skewed; mode for categorical. Geometric and harmonic means require positive values.