Statistics Calculator

Calculate comprehensive statistics including mean, median, mode, standard deviation, variance, and more from your data set.

About Statistics

Measures of Central Tendency

• Mean (x̄): The average of all values. Sum all numbers and divide by count.
• Median: The middle value when data is sorted. For even counts, average of two middle values.
• Mode: The most frequently occurring value(s) in the data set.

Measures of Spread

• Range: The difference between the maximum and minimum values.
• Variance (σ²): Average of squared differences from the mean. Measures data spread.
• Standard Deviation (σ): Square root of variance. Same units as original data.
• Sample Variance (s²): Variance calculated for a sample (divides by n-1 instead of n).
• Sample Std Dev (s): Square root of sample variance.

Formulas

• Mean: x̄ = Σx / n
• Population Variance: σ² = Σ(x - x̄)² / n
• Sample Variance: s² = Σ(x - x̄)² / (n - 1)
• Standard Deviation: σ = √(σ²)

When to Use Population vs Sample Statistics

• Population: Use when you have data for the entire population you're studying.
• Sample: Use when your data is a sample from a larger population (most common).

Examples

• Test scores: [85, 90, 78, 92, 88] → Mean: 86.6, Median: 88, Range: 14
• Temperatures: [20, 22, 19, 23, 21] → Mean: 21, Std Dev: 1.41
• Sales data: [100, 150, 100, 200, 150, 100] → Mode: 100, Median: 125