Enter dataset and display options
Paste numbers separated by commas, spaces, semicolons, or new lines. Then choose your bin rule, boundaries, and display precision.
Example data table
Use this sample to test the calculator quickly. These values create a distribution that works well with a histogram and bell curve overlay.
| Index | Value | Index | Value | Index | Value | Index | Value |
|---|---|---|---|---|---|---|---|
| 1 | 12 | 2 | 13 | 3 | 13 | 4 | 14 |
| 5 | 15 | 6 | 15 | 7 | 16 | 8 | 16 |
| 9 | 16 | 10 | 17 | 11 | 17 | 12 | 18 |
| 13 | 18 | 14 | 18 | 15 | 19 | 16 | 19 |
| 17 | 20 | 18 | 21 | 19 | 21 | 20 | 22 |
| 21 | 23 | 22 | 24 | 23 | 24 | 24 | 25 |
Formula used
The histogram groups values into equal-width bins across a chosen interval.
Bin width: h = (Upper Boundary - Lower Boundary) / k
Mean: μ = Σx / n
Sample variance: s² = Σ(x - x̄)² / (n - 1)
Sample standard deviation: s = √s²
Normal density: f(x) = [1 / (s√(2π))] × e^(-(x - x̄)² / 2s²)
Scaled bell curve: y = n × h × f(x)
That scaling matches the bell curve height to histogram frequencies, making visual comparison easier.
How to use this calculator
- Enter your dataset in the values box.
- Choose a bin rule or set a manual bin count.
- Optionally define lower and upper boundaries.
- Select how many decimals you want displayed.
- Press Generate Histogram to calculate results.
- Review the summary, chart, and frequency table.
- Use the CSV and PDF buttons to save the report.
Frequently asked questions
1. What does the bell curve represent here?
It shows a normal distribution fitted from your sample mean and sample standard deviation. It is a visual reference, not proof that your data is perfectly normal.
2. Which bin method should I choose?
Sturges works well for many small and medium datasets. Square root is simple. Rice often gives more bins. Manual mode is best when you need strict control.
3. Why does the chart use frequencies instead of probabilities?
Frequencies are easier to compare with raw counts. The overlaid bell curve is scaled by sample size and bin width to match those frequencies visually.
4. Can I use decimals and negative values?
Yes. The parser accepts integers, decimals, and negative numbers. Separate them with commas, spaces, semicolons, or line breaks.
5. Why is there no bell curve for some datasets?
If every value is identical, the standard deviation becomes zero. A normal curve cannot spread across the x-axis in that situation.
6. What do lower and upper boundaries do?
They let you control the histogram interval. The chosen boundaries must still include your complete dataset, or the calculator will show a validation warning.
7. Is the standard deviation sample-based or population-based?
This page uses the sample standard deviation. That choice is common when your values represent a sample from a larger population.
8. What can I do with the exported files?
The CSV file is useful for spreadsheets and reports. The PDF file is convenient for sharing, printing, presentations, or documentation.