Mean Calculator

Calculate arithmetic, geometric, harmonic, and weighted means with detailed explanations and statistical insights

Data Input

Enter positive numbers for geometric and harmonic means

Results

Enter data values and click "Calculate Mean" to see the results

Understanding Different Types of Means

Arithmetic Mean

The most common type of average. Simply add all values and divide by the count of values.

Formula: x̄ = (x₁ + x₂ + ... + xₙ) / n
Best for: General purpose averaging, normally distributed data

Geometric Mean

Used for rates, percentages, and multiplicative processes. Takes the nth root of the product of all values.

Formula: GM = ⁿ√(x₁ × x₂ × ... × xₙ)
Best for: Growth rates, ratios, percentage changes

Harmonic Mean

Used for rates and ratios. Calculated as the reciprocal of the arithmetic mean of reciprocals.

Formula: HM = n / (1/x₁ + 1/x₂ + ... + 1/xₙ)
Best for: Rates, speeds, densities, price-to-earnings ratios

Weighted Mean

Gives different importance (weights) to different values based on their significance.

Formula: x̄w = Σ(wᵢ × xᵢ) / Σwᵢ
Best for: Grades with different credits, portfolio returns

When to Use Each Mean

Arithmetic Mean

  • • Test scores and grades
  • • Temperature readings
  • • Height and weight measurements
  • • General statistical analysis

Geometric Mean

  • • Investment returns
  • • Population growth rates
  • • Inflation rates
  • • Index calculations

Harmonic Mean

  • • Average speed calculations
  • • Financial ratios (P/E ratios)
  • • Resistance in parallel circuits
  • • Machine learning (F1 score)

Weighted Mean

  • • Course grades with credits
  • • Portfolio performance
  • • Survey responses
  • • Quality control metrics

Key Properties

  • • HM ≤ GM ≤ AM (inequality)
  • • Arithmetic most sensitive to outliers
  • • Harmonic least affected by large values
  • • Geometric best for multiplicative data

Common Mistakes

  • • Using arithmetic for rates
  • • Negative values in geometric/harmonic
  • • Wrong weights in weighted mean
  • • Ignoring data distribution

Applications

  • • Statistical analysis
  • • Financial modeling
  • • Engineering calculations
  • • Academic grading
  • • Performance metrics

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