Histogram Maker and Frequency Distribution Table
Paste test scores, survey answers or any list of numbers to get a frequency table with counts, relative frequencies and cumulative frequencies, plus a histogram. Bin width and start value can be automatic or set by hand, and each bin includes its lower bound but not its upper bound. Copy the table as TSV or CSV, and save the chart as a PNG. Your data is processed in your browser and never uploaded. For the mean and standard deviation, try the Statistics Calculator.
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Enter numbers separated by commas, spaces, tabs or new lines (up to 10,000; you can paste a spreadsheet column). Anything that is not a number is ignored.
Leave blank to pick a round width that suits the amount of data.
Lower bound of the first bin. Blank rounds down to a multiple of the bin width.
Frequency table
| Bin [lower, upper) | Midpoint | Frequency | Relative (%) | Cumulative | Cumulative relative (%) |
|---|
How to use
- Paste your numbers into "Data (numbers)"
- Optionally enter "Bin width" and "Start value" (blank means automatic)
- Check the frequency table and histogram, and adjust the title and Y-axis
- Press "Save as PNG" to save the chart, or copy the table as TSV or CSV
Notes
- Each bin includes its lower bound and excludes its upper bound (left-closed, right-open). With a width of 10 and a start of 0, the value 10 falls in the bin 10 to 20.
- Bins are created up to the one that contains the maximum value, so no data point is dropped at the right edge.
- Up to 200 bins and 10,000 values are supported.
- If you set a start value above the minimum, values below it are left out of the counts.
- The automatic bin width uses Sturges' rule (bins ≈ 1 + log2 n) to pick a target number of bins and divides the data range by it, rounded to a round number. It is only a starting point, so adjust it for readability.
- Relative and cumulative relative frequencies are rounded to two decimals in percent, so the displayed values may not add up to exactly 100.
- With "Transparent background" on, the saved PNG has a transparent background.
Glossary
Bin and bin width
A bin is one interval the data is grouped into, and its size is the bin width. Here each bin includes its lower bound but not its upper bound.
Frequency and relative frequency
Frequency is the number of values in a bin. Relative frequency is that count divided by the total number of values.
Cumulative frequency
The running total of frequencies from the first bin up to the current bin. Divided by the total, it becomes the cumulative relative frequency.
Sturges' rule
A rule of thumb that suggests about 1 + log2(n) bins for n data points.
FAQ
Which bin does a value on a boundary go into?
Bins include their lower bound and exclude their upper bound. With a width of 10 and a start of 0, the value 10 is counted in the 10 to 20 bin, not 0 to 10. If the maximum sits exactly on a boundary, a final bin is added to hold it.
How should I choose the bin width?
Leave it blank and the tool uses Sturges' rule to estimate the number of bins, then picks a round width for your data range. If the shape looks too coarse or too noisy, try a smaller or larger width by hand and compare.
Why do some values disappear when I set a start value?
Values below the start value fall into no bin and are left out of the counts. The number left out is shown above the table. To keep everything, leave the start blank or set it at or below the minimum.
I get a "too many bins" error.
Up to 200 bins are allowed. Your bin width may be too small, or an outlier may be stretching the range. Use a larger bin width or adjust the start value.
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