Mean, Median & Mode Calculator

Enter a dataset to calculate measures of central tendency, spread, and distribution shape. Supports comma-separated, space-separated, or newline-separated values.

Separate values with commas, spaces, or newlines. Non-numeric entries are ignored.

Formulas Used

Mean (Arithmetic Average)

x̄ = (x₁ + x₂ + … + xn) / n

The sum of all values divided by the number of values.

Median

Odd n: median = x(n+1)/2  |  Even n: median = (xn/2 + xn/2+1) / 2

The middle value when data is sorted in order.

Mode

The value that appears most frequently in the dataset. A dataset can be unimodal (one mode), bimodal (two modes), multimodal, or have no mode if all values occur equally often.

Population Variance & Standard Deviation

σ² = ∑(xi − μ)² / N   |   σ = √σ²

Use when your data represents the entire population.

Sample Variance & Standard Deviation

s² = ∑(xi − x̄)² / (n − 1)   |   s = √s²

Use when your data is a sample drawn from a larger population. The (n − 1) denominator (Bessel's correction) produces an unbiased estimate.

Understanding Central Tendency

Mean, median, and mode are the three primary measures of central tendency—statistics that describe the center or typical value of a dataset. Each measure captures a different aspect of "center" and is useful in different situations.

When to Use Each Measure

Mean

  • • Best for symmetric distributions without outliers
  • • Uses every data point in the calculation
  • • Most common in scientific and financial analyses
  • • Sensitive to extreme values (outliers)

Median

  • • Best for skewed distributions or data with outliers
  • • Represents the "typical" value in income or housing data
  • • Not affected by extreme values
  • • Ideal for ordinal data

Mode

  • • Best for categorical or discrete data
  • • Identifies the most common value or category
  • • Useful in retail (most popular size, color, etc.)
  • • A dataset can have multiple modes or none

Relationship Between Mean, Median, and Mode

  • Symmetric distribution: Mean ≈ Median ≈ Mode. All three measures converge to the same value.
  • Right-skewed (positive skew): Mode < Median < Mean. The tail stretches to the right, pulling the mean higher.
  • Left-skewed (negative skew): Mean < Median < Mode. The tail stretches to the left, pulling the mean lower.

Worked Example

  • Dataset: 2, 4, 4, 5, 7, 7, 7, 9
  • Mean: (2 + 4 + 4 + 5 + 7 + 7 + 7 + 9) / 8 = 45 / 8 = 5.625
  • Median: Average of 4th and 5th values = (5 + 7) / 2 = 6
  • Mode: 7 (appears 3 times)
  • Range: 9 − 2 = 7

References

The formulas and definitions used in this calculator follow standard statistical practice:

Related Calculators

Median CalculatorMoving Average CalculatorConfidence Interval CalculatorPercentage Calculator

Note: This calculator automatically filters out non-numeric values. Population variance divides by N, while sample variance divides by (N-1) using Bessel's correction. Quartiles are computed using the inclusive median (interpolation) method. For critical analyses, verify results with professional statistical software.

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