Statistics Calculator

Calculate mean, median, mode, standard deviation, and variance for any dataset.

Why & What

Statistics is the mathematical discipline that helps us understand and interpret data. When you have a collection of numbers—test scores, temperatures, prices, or any measurements—statistics provides tools to summarize that data into meaningful numbers.

Mean (average) tells you the central tendency by adding all values and dividing by the count. Median is the middle value when data is sorted, useful when outliers exist. Mode is the most frequently occurring value. Standard Deviation measures how spread out the values are from the mean.

Formulas

Mean (x̄) = Σxᵢ / n
Sum of all values divided by the count of values
Median = Middle value of sorted data
If n is even: average of two middle values
σ = √[Σ(xᵢ - x̄)² / n]
Population Standard Deviation
s = √[Σ(xᵢ - x̄)² / (n-1)]
Sample Standard Deviation (Bessel's correction)

Calculator

Educational Purpose Only: This calculator is provided for learning and educational purposes. For critical applications or professional use, please verify results with appropriate professional tools and expertise.

How to Read Results

Mean: If your dataset is {10, 20, 30}, the mean is 20. This represents the "average" value. Values far from the mean are considered unusual.

Median: The median is the "middle" value. For {10, 20, 100}, the median is 20, while the mean would be 43.33. Median is more resistant to outliers.

Mode: Shows which value(s) appear most frequently. A dataset can have no mode, one mode (unimodal), or multiple modes (multimodal).

Standard Deviation: A low value means data points cluster close to the mean; a high value means they're spread out. For normally distributed data, about 68% of values fall within 1 standard deviation of the mean.

Example

Test Scores Analysis

A class has the following test scores: 72, 85, 90, 78, 85, 92, 88, 85, 76, 89

Results:

  • Mean: 84.0 (average score)
  • Median: 85.0 (middle score)
  • Mode: 85 (most common score, appears 3 times)
  • Population Std Dev: 6.16 (scores vary by about 6 points)

This tells us the class performed fairly consistently, with most students scoring between 78 and 90.

Limitations & Disclaimer

Important Limitations
  • This calculator is for educational purposes only.
  • Mean can be misleading when outliers are present—consider using median instead.
  • Mode may not exist for datasets with all unique values.
  • Standard deviation assumes a reasonably symmetric distribution for meaningful interpretation.
  • Use "Sample" standard deviation when your data represents a sample from a larger population.
  • Results should be verified for critical applications.