| # | Value |
|---|---|
| 1 | 12 |
| 2 | 13 |
| 3 | 15 |
| 4 | 15 |
| 5 | 18 |
| 6 | 21 |
| 7 | 22 |
| 8 | 22 |
| 9 | 25 |
| 10 | 27 |
| Class interval | Frequency |
|---|---|
| [12, 15) | 2 |
| [15, 18) | 2 |
| [18, 21) | 1 |
| [21, 24) | 3 |
| [24, 27] (last includes max) | 2 |
- Frequency (fᵢ): count of values inside class i.
- Relative frequency (rᵢ): rᵢ = fᵢ / n.
- Percent (pᵢ): pᵢ = 100 × rᵢ.
- Cumulative frequency (Fᵢ): Fᵢ = Σⱼ≤ᵢ fⱼ.
- Bin width (for k bins): w = (max − min) / k.
- Sturges: k = ⌈log₂(n) + 1⌉.
- Scott: w = 3.5 × s / n^(1/3), then k = ⌈range / w⌉.
- Freedman–Diaconis: w = 2 × IQR / n^(1/3), then k = ⌈range / w⌉.
- Paste your values into the input box using any separators.
- Choose Auto, Numeric, or Categorical depending on your data.
- For numeric data, select a binning method or set custom bins.
- Optionally override min or max to align class boundaries.
- Press Submit to view the distribution below the header.
- Use the download buttons to export CSV or PDF reports.
Overview
Frequency distribution converts raw observations into a summary of how often values appear. It highlights concentration, gaps, and repetition before you draw any chart. For numeric datasets, grouping into class intervals supports stable summaries when the sample size grows. For categorical datasets, counting unique labels reveals dominant segments and long tails. This calculator reports frequency, relative frequency, percent, and cumulative totals for consistent comparisons. Works for surveys, logs, and measurements alike.
Binning
Class design drives interpretation, so the binning rule matters. Sturges grows the bin count with log₂(n), working well for small to medium samples. Scott sets bin width from the sample standard deviation, producing smoother histograms for near normal data. Freedman–Diaconis uses the interquartile range, making width more robust to outliers. When reporting needs fixed bands, use custom bins, custom width, and optional min or max overrides for operational reporting.
Metrics
Relative frequency rᵢ = fᵢ/n approximates probability mass within each class, and percent makes outputs presentation ready. Cumulative frequency Fᵢ = Σⱼ≤ᵢ fⱼ helps locate thresholds, such as the class that contains the 80th percentile. For numeric tables, midpoints provide a representative value for quick comparisons between intervals. For categories, sorting by frequency surfaces top contributors, while alphabetical sorting supports audits and dictionary checks. Percent and cumulative views help communicate findings without charts.
Diagnostics
Grouped counts make distribution shape easier to diagnose. A long right tail across the final classes suggests positive skew, while heavy early classes suggest negative skew. Compare mean and median to confirm asymmetry, and inspect bins with low frequency for rare events or input mistakes. If a single extreme value stretches the range, Scott and Sturges may create wide classes. Use min and max overrides to explore class boundaries during validation.
Reporting
Sharing results is simpler when the table is exportable. Download a CSV to filter, merge, and model the distribution in other analytics workflows. Download a PDF to capture a snapshot for stakeholders, including the timestamp and table. For reproducibility, record the chosen rule, the final bin count k, the computed width w, and display decimals. Use the example section to document inputs, then interpret the grouped output consistently with confidence reliably.
What separators can I use for input?
Paste values separated by commas, spaces, tabs, or new lines. Semicolons also work. Mixed separators are fine because the parser normalizes them before analysis.
When should I switch to categorical mode?
Use categorical mode for labels such as channels, regions, or status codes. It counts each distinct label and can sort by frequency or alphabetically. If your data includes non-numeric tokens, auto-detect will choose this mode.
Which binning rule should I start with?
Start with Sturges for quick baselines on smaller samples. For larger numeric sets, Scott often smooths well, while Freedman–Diaconis resists outliers by using IQR. If reporting needs fixed bands, choose custom bins or width.
Why does the last class include the maximum?
Intervals are built as [lower, upper) to avoid double counting boundary values. The final class is treated as inclusive of the maximum so your highest observation is never excluded from the table.
How do min and max overrides affect results?
Overrides replace the automatically detected boundaries, changing the range and therefore the computed class edges. Values outside the overridden range are ignored in the numeric table, which is useful when you want to focus on a target operating window.
What is included in the CSV and PDF exports?
CSV contains the full distribution table with frequencies, relative values, percents, and cumulative totals. PDF provides a formatted snapshot with a timestamp and the same rows, suitable for sharing or attaching to documentation.