Statistics Calculator

Calculate mean, median, mode, standard deviation, variance, and more from a dataset. This tool processes all data locally in your browser. No information is ever sent to any server. Completely free, no registration required.

How to Use the Statistics Calculator

1. Enter your input values above
2. Results update automatically
3. Copy or download the output

What is a Statistics Calculator?

A Statistics Calculator computes all fundamental descriptive statistics from a dataset: mean, median, mode, range, variance, standard deviation, quartiles, skewness, kurtosis, and more. It's the tool students use to check their work, data analysts use for quick exploratory data analysis (EDA), and anyone uses when they have a list of numbers and need to understand its distribution. The calculator also generates a box-and-whisker plot summary and identifies outliers using the 1.5×IQR rule.

How Does It Work?

Enter numbers separated by commas, spaces, or newlines. The calculator instantly computes: (1) Measures of Central Tendency: mean (average), median (middle value), mode (most frequent), (2) Measures of Dispersion: range, variance, standard deviation (population and sample), IQR (interquartile range), (3) Shape: skewness, kurtosis, (4) Position: quartiles (Q1, Q2, Q3), percentiles (any), min, max. A five-number summary (min, Q1, median, Q3, max) is displayed for box plot construction.

Formula

Descriptive Statistics:\n\nMean (x̄) = Σxᵢ ÷ n\nMedian = middle value when sorted (or average of two middle values if n is even)\nMode = most frequent value(s)\n\nPopulation Variance (σ²) = Σ(xᵢ − x̄)² ÷ n\nSample Variance (s²) = Σ(xᵢ − x̄)² ÷ (n−1)\nStandard Deviation = √variance\n\nPercentile P: value at position P/100 × (n+1) when sorted\nQ1 = 25th percentile, Q2 = 50th (median), Q3 = 75th\nIQR = Q3 − Q1\n\nOutlier Detection (Tukey's Fences):\n• Lower Fence = Q1 − 1.5 × IQR\n• Upper Fence = Q3 + 1.5 × IQR\n• Values outside fences are outliers\n\nFive-Number Summary: [Min, Q1, Median, Q3, Max]\n\nSkewness = indicates asymmetry: positive = right tail, negative = left tail\nKurtosis = indicates tail heaviness: normal = 3, >3 = heavy tails

Who Uses This Tool?

• Students solving statistics homework and verifying manual calculations
• Data analysts performing quick EDA before committing to a full analysis
• Researchers summarizing experimental data for publications
• Business analysts computing summary statistics for quarterly reports
• Anyone with a list of numbers wanting to understand the distribution

Pro Tips

• Use sample standard deviation (n−1) when your data is a sample of a larger population; use population (n) when you have every data point
• Always check for outliers before drawing conclusions — one extreme value can dramatically skew the mean while the median stays robust
• The five-number summary is the foundation of a box plot: draw a box from Q1 to Q3, with a line at the median, whiskers to min/max (excluding outliers)
• For small datasets (<30 values), many statistics are unreliable. Sample size matters — be cautious interpreting skewness or kurtosis with <50 data points

Frequently Asked Questions about Statistics Calculator

Should I use population or sample standard deviation?

Use sample (STDEV.S, n−1) when working with a subset of a larger population — which is most real-world data. Use population (STDEV.P, n) only when you have data for the entire population (e.g., test scores for every student in a class).

What's the difference between variance and standard deviation?

Variance (σ²) is in squared units; standard deviation (σ) is the square root of variance and is in the original units. Standard deviation is more intuitive because it's on the same scale as the data. A dataset with mean 100 and SD 15 means most values fall between 85-115.

Free online Statistics Calculator — no signup, 100% client-side processing. All data stays in your browser.