Mean Calculator
Calculate arithmetic, geometric, and harmonic means with step-by-step explanations
Calculate Statistical Means
Use weights to give different importance to each value
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Example Calculations
Test Scores Example
Values: 85, 92, 78, 96, 89
Arithmetic Mean: (85+92+78+96+89)/5 = 88
Use Case: Average test score in a class
Investment Returns Example
Values: 1.05, 1.12, 0.95, 1.08 (growth factors)
Geometric Mean: ⁴√(1.05×1.12×0.95×1.08) = 1.049
Use Case: Average annual return rate
Speed Example
Values: 60, 30 mph (different speeds)
Harmonic Mean: 2/(1/60 + 1/30) = 40 mph
Use Case: Average speed for equal distances
Types of Means
Arithmetic Mean
Sum ÷ Count
Most common average
Geometric Mean
nth root of product
For growth rates
Harmonic Mean
n ÷ (sum of reciprocals)
For rates and speeds
Calculator Tips
Enter up to 50 values for calculation
Geometric and harmonic means require positive values
Use weighted means when values have different importance
Choose specific mean types for faster calculation
Understanding Statistical Means
What is a Mean?
A mean is a measure of central tendency that represents the typical value in a dataset. Different types of means are suited for different types of data and applications, each providing unique insights into your data distribution.
When to Use Each Mean
- •Arithmetic: General purpose, test scores, temperatures
- •Geometric: Growth rates, investment returns, ratios
- •Harmonic: Rates, speeds, frequencies
Mathematical Formulas
Arithmetic Mean
A = (x₁ + x₂ + ... + xₙ) / n
Geometric Mean
G = ⁿ√(x₁ × x₂ × ... × xₙ)
Harmonic Mean
H = n / (1/x₁ + 1/x₂ + ... + 1/xₙ)
Mean Inequality: For positive values, H ≤ G ≤ A, with equality only when all values are identical.
Weighted Means
Weighted means allow you to assign different levels of importance to each value in your dataset. This is particularly useful when calculating GPAs (where credits serve as weights), stock portfolio returns (where investment amounts serve as weights), or survey results (where response frequency serves as weights).
Weighted Arithmetic
Σ(wᵢxᵢ) / Σwᵢ
Common in GPA calculations
Weighted Geometric
∏(xᵢ^wᵢ)^(1/Σwᵢ)
Used in financial indices
Weighted Harmonic
Σwᵢ / Σ(wᵢ/xᵢ)
For weighted averages of rates