Turn raw numbers into clear, comparable insights fast. Choose sample or population, set rounding easily. Download tables as CSV or PDF for sharing anywhere.
| Row | Value | Comment |
|---|---|---|
| 1 | 12 | Low-end observation |
| 2 | 15 | Early cluster |
| 3 | 18 | Rising trend |
| 4 | 22 | Central mass |
| 5 | 22 | Repeat value (mode candidate) |
| 6 | 30 | High-end point |
Use the “Load example data” button to analyze these values instantly.
Descriptive summaries convert messy observations into comparable indicators. In analytics reviews, teams scan count, minimum, maximum, and range to spot missing coverage, unit mistakes, and duplicated rows. A sudden 10× jump in max often flags a scaling change. When n is small, a single extreme can dominate, so pairing range with quartiles and percentiles provides a steadier view of typical behavior and data quality.
Mean and median answer different questions. The mean tracks overall level and reacts strongly to outliers, while the median reflects the midpoint of the ordered data and stays stable under spikes. If the mean exceeds the median, high values may be pulling the distribution right; the reverse suggests low-end pressure. Mode is useful for repeated measurements such as common order sizes or recurring sensor states. If there is no repeat, leaving mode blank is more honest than forcing one.
Variance and standard deviation quantify dispersion around the mean. For sample data, dividing Σ(x−x̄)² by n−1 reduces bias; for complete populations, dividing by n is appropriate. Standard error equals standard deviation divided by √n, shrinking as the dataset grows. A quick mean interval using z·SE (often 1.96 for 95%) helps detect practical shifts during weekly monitoring. Consistent rounding, such as four decimals, prevents false differences across exported reports.
Percentiles and the interquartile range expose tail behavior better than one average. Q1, Q3, and IQR summarize the middle 50% and support Tukey fences: Q1−k·IQR and Q3+k·IQR, with k=1.5 as a common rule. Trimming outside these fences can stabilize dashboards, but always record how many points were removed. Add 5th and 95th percentiles to monitor tail drift without overreacting. Skewness indicates asymmetry, and excess kurtosis highlights unusually heavy or light tails.
Use the coefficient of variation to compare volatility across metrics with different units; it expresses spread relative to |mean|. Geometric mean supports growth factors and ratios, but only for positive values, while harmonic mean suits rates when values are nonzero. Combine trimming, rounding, and chosen percentiles to produce consistent, audit-friendly exports for analysts, managers, and stakeholders. Sharing the same CSV and PDF improves reproducibility.
Paste values separated by commas, spaces, tabs, or new lines. Decimals and scientific notation are accepted. Non-numeric tokens are ignored, so review the cleaned preview to confirm everything parsed as expected.
Use sample when the data is a subset and you want an unbiased variance estimate using n−1. Use population when you have the complete set and variance should be divided by n.
Percentiles are computed on sorted values using type‑7 linear interpolation. This matches common spreadsheet behavior and provides smooth results even when the requested percentile falls between observed points.
When enabled, values outside Tukey fences are removed before calculations. Fences are Q1−k·IQR and Q3+k·IQR. Trimming can stabilize summaries, but you should document how many points were excluded.
Geometric mean requires all values to be positive, because it uses logarithms. Harmonic mean requires all values to be nonzero, because it uses reciprocals. If conditions fail, the calculator displays a dash.
No. The interval uses a normal approximation, Mean ± z·SE, to provide a quick uncertainty band. For small samples or non-normal data, consider robust intervals or resampling methods.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.