Sample vs. population
Population variance divides squared deviations by n. Sample variance divides by n − 1 to estimate population variance from a sample. The calculator always shows both and highlights your selected convention.
PASTE · SUMMARIZE · INTERPRET
Statistics Calculator
Turn a raw data set into a full descriptive-statistics report: center, spread, quartiles, outliers, shape, percentiles, frequency table, histogram and box plot — with sample/population choices made explicit.
30+summary measures
2 inputsraw or frequency
localno upload
DESCRIPTIVE STATISTICS WORKBENCH
Paste the data you actually have
Commas, spaces, tabs, semicolons and new lines work. Spreadsheet columns paste directly. Invalid tokens are rejected instead of silently ignored.
One row per value. Frequencies must be positive whole numbers. This mode is useful for grouped classroom tables and repeated measurements.
FULL REPORT
Quartiles: inclusive linear.Center, spread, position and shape
Center
- Count (n)
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- Sum
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- Mean
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- Median
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- Mode(s)
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- Midrange
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- Geometric mean
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- Harmonic mean
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Spread
- Min / Max
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- Range
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- Population variance
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- Population SD
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- Sample variance
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- Sample SD
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- Standard error
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- RMS
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Position & robust spread
- P10 / P90
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- Q1 / Q3
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- IQR
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- Outlier fences
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- Outliers
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- Mean abs. deviation
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- Median abs. deviation
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- Robust σ ≈ 1.4826 MAD
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Shape
- Sample skewness
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- Population skewness
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- Sample excess kurtosis
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- Population excess kurtosis
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- Coefficient of variation
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- Sum of squared deviations
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- Data order
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- Distinct values
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HISTOGRAM
See the distribution
Bars show counts; mean and median are marked.
BOX PLOT
Quartiles & outliers
Whiskers stop at the most extreme non-outlier values under the 1.5×IQR rule.
Z-score & percentile rank
Z-SCORE—
PERCENTILE RANK—
Uses the selected sample/population SD for z-score.
Counts and shares
| Value | Count | Share | Cumulative |
|---|---|---|---|
| Calculate to see frequencies. | |||
Show the working & interpretation
- Enter values above.
DAILY STATISTICS
One small data set per UTC day
Same values for everyone on the date. Estimate the requested statistic, then check yourself.
TODAY'S DATA—
Which answer is correct?
Choose an answer.
Methods, formulas & scope
Quartile methods
Different textbooks and software can disagree on Q1/Q3. Choose inclusive linear interpolation, Tukey median-of-halves, or an exclusive (n+1) rule; the selected method is stated beside the report.
Shape statistics
Skewness summarizes asymmetry. Excess kurtosis compares tail/peak behavior with a normal distribution baseline of 0. Small data sets can make both unstable, so interpret them cautiously.
Privacy & limits
Everything runs locally. Raw mode accepts up to 100,000 values; frequency mode expands up to 200,000 observations. This is a descriptive-statistics learning tool, not a replacement for a validated statistical package in regulated or high-stakes analysis.