Statistics Calculator: Mean, Median, Mode, and S...

Descriptive Statistics

Descriptive statistics summarize and describe a dataset with numerical measures. They capture the center (mean, median, mode), spread (standard deviation, variance, range), and shape (skewness) of data distributions. These are fundamental to data science, scientific research, quality control, and academic study.

📈 Statistics Calculator

Use our free calculator for instant, accurate results.

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📐 Formula

σ = √[Σ(xᵢ − μ)² / N]

σ = population standard deviation, μ = population mean, N = number of data points. For sample: divide by (N−1) instead. Mean: μ = Σxᵢ/N.

📝 Worked Example

Dataset: {2, 4, 4, 4, 5, 5, 7, 9}
Mean = 40/8 = 5.0
Median = (4+5)/2 = 4.5
Mode = 4
Variance = [(9+1+1+1+0+0+4+16)/8] = 4
Std Dev = 2

📝 How to Use the Calculator

Enter DataType your numbers separated by commas, spaces, or line breaks.

CalculateView all descriptive statistics simultaneously.

Sample vs PopulationToggle between sample (÷N−1) and population (÷N) standard deviation.

View DistributionSee histogram and summary statistics card.

❓ FAQ

What is the difference between mean and median?

Mean is sensitive to outliers (extreme values). Median (middle value) is robust to outliers. For skewed data (like income), median is a more representative "average".

When should I use standard deviation vs variance?

Variance (σ²) is used mathematically (e.g., in ANOVA). Standard deviation (σ) is preferred for reporting as it has the same units as the original data.

Descriptive Statistics