Enter Histogram Inputs
Example Data Table
This sample dataset represents 20 observed values that can be pasted directly into the calculator.
| Observation 1 | Observation 2 | Observation 3 | Observation 4 | Observation 5 |
|---|---|---|---|---|
| 12 | 15 | 16 | 17 | 18 |
| 18 | 19 | 20 | 20 | 21 |
| 22 | 22 | 23 | 24 | 24 |
| 25 | 26 | 27 | 28 | 30 |
Formula Used
- Range: Range = Maximum − Minimum
- Class Width: Bin Width = (Upper Bound − Lower Bound) ÷ Number of Bins
- Relative Frequency: Relative Frequency = Bin Count ÷ Total Included Values
- Frequency Density: Density = Bin Count ÷ (Total Included Values × Bin Width)
- Midpoint: Midpoint = (Lower Class Limit + Upper Class Limit) ÷ 2
- Sturges Rule: k = ceil(log2(n) + 1)
- Scott Rule: Width = 3.5 × s ÷ n^(1/3)
- Freedman–Diaconis Rule: Width = 2 × IQR ÷ n^(1/3)
How to Use This Calculator
- Paste or type your raw numeric observations into the data box.
- Choose an automatic or manual binning method.
- Set optional lower and upper bounds if you want trimming.
- Select count, relative frequency, or density for bar height.
- Pick the number of displayed decimals for cleaner reports.
- Press Generate Histogram to see the chart and grouped table above the form.
- Use the CSV and PDF buttons to export your grouped histogram output.
Why this histogram tool is useful
A histogram summarizes shape, spread, clustering, skewness, and gaps in one view. It helps compare distributions, validate assumptions, and present raw measurements in grouped form for classes, audits, quality checks, and exploratory analysis.
FAQs
1. What data works best in this histogram generator?
Use continuous or discrete numeric observations entered as raw values. Histograms are best for measurements, scores, durations, costs, weights, and similar quantitative datasets.
2. What does the auto binning option do?
Auto binning selects a practical bin count from your sample. This file prefers Freedman–Diaconis when spread information is stable, then falls back to Sturges when necessary.
3. When should I use manual bins?
Use manual bins when class widths must match a report, textbook, or regulation. It is also helpful when you want consistent intervals across multiple datasets.
4. What is frequency density?
Frequency density adjusts counts for class width. It becomes important when comparing histograms with unequal intervals because taller bars then represent greater concentration, not only larger counts.
5. Why are some values excluded?
Values are excluded only when you set lower or upper bounds. The summary section tells you how many observations were trimmed from the histogram calculation.
6. Does this calculator show skewness?
Yes. It reports sample skewness along with quartiles, mean, median, and standard deviation, helping you judge whether the distribution leans left, right, or stays balanced.
7. Can I export the grouped output?
Yes. After calculation, use the CSV button for spreadsheet work or the PDF button for reports, classrooms, client summaries, and quick documentation.
8. Is this tool suitable for teaching statistics?
Yes. It combines raw input, histogram drawing, grouped frequencies, and descriptive statistics, making it useful for practice problems, assignments, demonstrations, and revision.