Mean Calculator
Result
About Means
Means are measures of central tendency that represent the average value of a set of numbers. Different types of means are used for different purposes.
Types of Means:
| Type | Formula | Use Case |
|---|---|---|
| Arithmetic Mean | (x₁ + x₂ + ... + xₙ) / n | General purpose average, most common |
| Geometric Mean | ⁿ√(x₁ × x₂ × ... × xₙ) | Growth rates, ratios, percentages |
| Harmonic Mean | n / (1/x₁ + 1/x₂ + ... + 1/xₙ) | Rates, speeds, ratios |
Examples:
| Numbers | Arithmetic Mean | Geometric Mean | Harmonic Mean |
|---|---|---|---|
| 2, 4, 8 | 4.67 | 4 | 3.43 |
| 1, 2, 4, 8 | 3.75 | 2.83 | 2.29 |
Properties:
- Arithmetic Mean ≥ Geometric Mean ≥ Harmonic Mean
- All means are equal when all numbers are equal
- Geometric mean is best for multiplicative relationships
- Harmonic mean is best for rates and ratios
Tips:
- Use arithmetic mean for general averages
- Use geometric mean for growth rates and percentages
- Use harmonic mean for rates and speeds
- All numbers must be positive for geometric and harmonic means
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