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Average Calculator

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Calculate Mean, Median, Mode, and More

Example: 1, 2, 3, 4, 5. Supports CSV paste from Excel.

Variance:

1. How to Use

  1. Enter numbers separated by commas or spaces. Example: 1, 2, 3, 4, 5. Supports CSV paste from Excel.
  2. Results update automatically as you type (real-time). Use Calculate, Reset, or Use sample data as needed.
  3. Set decimal places (0–6), thousands separator, and variance type (Sample / Population). Copy results to clipboard with one click.

2. How It Works

Mean: Sum ÷ Count. Median: Middle value when sorted. Mode: Most frequent value(s). Range: Max − Min.

Variance: Average of squared deviations from mean. Standard deviation: square root of variance. You can choose Sample (n−1) or Population (n) for variance calculation.

Quartiles (Q1, Q3): We use the median-of-halves method: split data at the median, then take the median of the lower half for Q1 and the median of the upper half for Q3. IQR = Q3 − Q1.

Geometric mean: (∏ x_i)^(1/n), requires all positive numbers. Harmonic mean: n / Σ(1/x_i), requires all positive non-zero numbers.

3. About Average Calculator

Free online average calculator with comprehensive statistics. Uses a single, consistent set of calculation methods (see below) so you get predictable, comparable results.

4. Advantages

  • 15+ statistics: Mean, Median, Mode, Min, Max, Range, Variance, Std Dev, Q1, Q3, IQR, Geometric Mean, Harmonic Mean.
  • Variance toggle: Choose Sample (n−1, default) or Population (n) to match your use case.
  • Clear calculation methods: All formulas are documented. Same input → same result, every time.

5. Real-World Use Cases

  • Academic: Grade analysis, test scores, research data.
  • Financial: Sales analysis, investment returns, market research.
  • Scientific: Experimental data, survey analysis, quality control.
  • Personal: Budget planning, fitness tracking, expense averages.

6. Calculation Methods (How We Compute Each Statistic)

We use one fixed method per statistic so that the same input always gives the same result. This reduces confusion when comparing with other tools or your own calculations.

Basic statistics

  • Mean (arithmetic average): Sum of all values ÷ number of values.
  • Median: The middle value when data is sorted. If even number of values, average of the two middle values.
  • Mode: The value(s) that appear most frequently. N/A when all values are unique.
  • Min / Max / Range: Smallest value, largest value, and Max − Min.

Variance & standard deviation

  • Sample variance (default): Σ(x − mean)² ÷ (n − 1). Use when your data is a sample drawn from a larger population. Matches Excel VAR.S, Google Sheets VAR.S.
  • Population variance: Σ(x − mean)² ÷ n. Use when your data includes the entire population.
  • Standard deviation: Square root of variance. Same formula, whether sample or population.

Quartiles (Q1, Q2, Q3) & IQR

  • Method: Median of lower/upper half (exclusive median). Commonly used in textbooks and box plots.
  • Step 1: Sort data. Find median (Q2).
  • Step 2: Q1 = median of the lower half (values below median, excluding median when n is odd).
  • Step 3: Q3 = median of the upper half (values above median, excluding median when n is odd).
  • IQR (interquartile range) = Q3 − Q1.

Geometric mean

  • Formula: (x₁ × x₂ × … × xₙ)^(1/n), or equivalently exp(Σ ln(xᵢ) / n).
  • Requires all values to be positive. Shows N/A if any value is zero or negative.
  • Useful when averaging ratios or multiplicative growth rates.

Harmonic mean

  • Formula: n / (1/x₁ + 1/x₂ + … + 1/xₙ).
  • Requires all values to be positive and non-zero. Shows N/A otherwise.
  • Useful for rates (e.g., average speed over equal distances).