Statistics Calculator
Calculate descriptive statistics from any dataset: Mean, Median, Mode, Standard Deviation, Variance, Quartiles (Q1, Q3), IQR, and Tukey outlier detection.
Enter Numbers or Paste Data
Central Tendency
⚖️ Decision Verdict: Slight Left Skew (Median > Mean)
The median (89.00) exceeds the mean (87.10), indicating lower scores pull the average downward. For skewed distributions, the median represents typical performance more reliably than the mean.
Dispersion, Quartiles & Outliers
About this tool
How to use it
- Paste or type your numbers into the raw values text box, separated by commas, spaces, or line breaks.
- Select your calculation mode: 'Sample' (using n - 1 degrees of freedom for sample standard deviation) or 'Population' (N).
- Optionally click 'Sort Ascending' to organize your dataset in numerical order.
- Click 'Compute Statistics' to view the Mean, Median, Mode, Standard Deviation, Variance, Quartiles, and IQR.
- Review Tukey outlier detection callouts to identify any statistical anomalies in your sample.
Why it matters
Descriptive statistics summarize and identify essential patterns within raw data points. Computing the mean alone can be deceptive if extreme values or outliers distort the distribution. Analyzing both central tendency (mean, median, mode) and dispersion (standard deviation, variance, interquartile range) gives an honest, complete picture of data spread and skewness.
When to use it
Use this tool when analyzing survey results, verifying lab experiments, studying coursework statistics, checking product manufacturing variance, or conducting scientific data checks.
Good to know
Sample vs Population: Always choose 'Sample' when analyzing a representative subset of a larger group, as Bessel's correction (dividing by n - 1 rather than n) corrects for underestimating true population variability.
Common questions
What is the difference between sample and population standard deviation?
Population standard deviation (σ) divides the sum of squared deviations by N (when you have data for every member of a group). Sample standard deviation (s) divides by n - 1 (Bessel's correction) to provide an unbiased estimate when analyzing a sample drawn from a larger population.
How does this calculator detect outliers?
Outliers are identified using John Tukey's standard interquartile rule: any value lower than Q1 - 1.5×IQR or higher than Q3 + 1.5×IQR is flagged as a statistical outlier.
What should I report: Mean or Median?
For normally distributed, symmetric data, the mean is standard. For skewed distributions (e.g. household income, real estate prices) or datasets containing extreme outliers, the median is much more representative.
What does an Interquartile Range (IQR) represent?
The IQR (Q3 - Q1) measures the spread of the middle 50% of your data. Unlike the range (Max - Min), IQR is resistant to extreme outliers.
Can I paste numbers directly from Excel or Google Sheets?
Yes! The parser accepts newline-separated columns, tab-separated values, and comma-separated lists automatically.