📊 Average & Statistics Calculator

Calculate mean, median, mode, range, standard deviation, variance, and more for any set of numbers.

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Mean (Average)
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Median
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Mode
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Range
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Std Deviation (σ)
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Variance (σ²)
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Count (n)
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Sum
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Min
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Max
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Understanding Statistical Measures

Measures of Central Tendency

  • Mean: Sum of all values divided by count. Most common "average." Sensitive to outliers.
  • Median: Middle value when sorted. Robust to outliers — often preferred for skewed data like income.
  • Mode: Most frequently occurring value. Can have multiple modes or none if all values are unique.

Measures of Dispersion

  • Range: Difference between max and min. Simple but sensitive to outliers.
  • Standard Deviation (σ): Average distance from the mean. The square root of variance. Higher values indicate more spread.
  • Variance (σ²): Average squared deviation from the mean. Squaring magnifies outliers and makes all values positive.
Mean (μ) = Σx / n
Variance (σ²) = Σ(x − μ)² / n
Standard Deviation (σ) = √variance
When should I use population vs sample standard deviation? +
Population std dev (σ) divides by n and is used when your data represents the entire population. Sample std dev (s) divides by n−1 (Bessel's correction) and is used when your data is a sample drawn from a larger population — this is more common in practice. This calculator uses population standard deviation.
Why is median often better than mean for income data? +
A small number of extremely high earners pull the mean income up significantly, making it appear higher than what most people actually earn. The median (the value where half earn more and half earn less) is not affected by these outliers, giving a more representative picture of typical income.