Calculator
Example data table
| # | Value |
|---|---|
| 1 | 12 |
| 2 | 15 |
| 3 | 14 |
| 4 | 18 |
| 5 | 21 |
| 6 | 13 |
| 7 | 16 |
| 8 | 19 |
| 9 | 17 |
| 10 | 20 |
Formulas used
- Mean = Σx / n
- Median = middle value (or average of two middles)
- Range = max − min
- Variance (population) = Σ(x−x̄)² / n
- Variance (sample) = Σ(x−x̄)² / (n−1)
- Std. deviation = √variance
- Standard error = s / √n
- Percentile(p) via linear interpolation between closest ranks
- IQR = Q3 − Q1
- Outlier fences = Q1 − k·IQR and Q3 + k·IQR
- Skewness uses adjusted Fisher–Pearson coefficient
- Kurtosis reports adjusted excess kurtosis
- CV = (s / |x̄|) × 100%
How to use this calculator
- Paste your numeric values in the dataset box.
- Choose whether your data represents a sample or population.
- Set decimals, percentiles, and optional trimmed mean.
- Adjust outlier factor to match your analysis policy.
- Press Submit to compute results above.
- Use the download buttons to export CSV or PDF.
Data preparation and validation
Descriptive summaries are only as reliable as the input. This calculator accepts commas, spaces, new lines, and scientific notation, then reports how many tokens were parsed and how many were discarded as invalid. Use that feedback to remove headers, unit labels, and stray punctuation. If you enable duplicate removal, the tool recomputes every metric on unique values only, which is useful for catalog-style datasets. If you paste formatted currency or grouped digits, the parser removes grouping marks, keeps signs, and preserves decimals for consistent calculations.
Interpreting central tendency
Mean and median answer different questions. The mean reflects the balance point of the dataset, while the median marks the 50th percentile and resists extreme values. When the gap between mean and median grows, the distribution is often skewed. Mode detection is precision-based, so values are rounded before counting repeats; increase precision for high-resolution sensors and reduce it for noisy measurements.
Understanding variability and uncertainty
Spread measures explain how wide the values are. Range is quick but sensitive to extremes, so pair it with standard deviation and the interquartile range. Choose sample variance for estimates from a subset (denominator n−1) and population variance when you have the full population (denominator n). Standard error equals s/√n, shrinking as n grows, and supports a 95% confidence interval for the mean.
Percentiles, distribution shape, and outliers
Percentiles are computed with linear interpolation between closest ranks, matching common spreadsheet behavior. Quartiles (Q1 and Q3) define the IQR, which is stable under outliers. The outlier fences use Q1 − k·IQR and Q3 + k·IQR; k=1.5 is a typical screening rule, while k=3 is a stricter definition. Skewness and excess kurtosis add context about asymmetry and tail heaviness.
Reporting and export workflow
For reproducible reporting, set a consistent decimal policy and percentile list across projects. After computing, export a CSV for downstream modeling or a PDF for audits and stakeholder packs. Include the parsed token counts to document cleaning decisions, and attach the cleaned, sorted preview to make verification easy. The included histogram uses Sturges bins to provide a compact, comparable distribution summary across timeframes too.
FAQs
1) What separators can I use for values?
Use commas, spaces, tabs, or new lines. You can paste a column from a spreadsheet. Scientific notation like 3.2e-4 is accepted, while non-numeric tokens are skipped and reported.
2) Should I choose sample or population variance?
Choose sample when your dataset is a subset and you want an unbiased variance estimate using n−1. Choose population when you have every member of the population and want variance divided by n.
3) How are percentiles calculated here?
Percentiles use linear interpolation between closest ranks, which matches common spreadsheet behavior. This provides smooth results for small datasets and avoids abrupt jumps that occur with pure nearest-rank methods.
4) What does the outlier factor control?
The tool flags values outside Q1 − k·IQR or Q3 + k·IQR. A factor of 1.5 is a typical screening rule; larger factors reduce flagged points, smaller factors increase sensitivity.
5) Why are geometric or harmonic means sometimes N/A?
Geometric mean requires all values to be greater than zero. Harmonic mean requires no zeros. If those conditions fail, the calculator returns N/A to prevent misleading summaries.
6) What is included in the CSV and PDF exports?
Exports include the main metrics, selected percentiles, optional confidence interval, and the cleaned sorted values. Use CSV for further analysis and the PDF for reports, reviews, or audit trails.