Quality Tools
Histogram Generator
See the shape of your data — centring, spread, skew, and outliers — and how it sits against specification limits.
Bulk Data Input
Paste multiple values separated by spaces, commas, or new lines:
Shaft Diameter Measurements
Central Tendency
Mean: 24.950
Median: 24.950
Mode: None
Variability
Std Dev: 0.227
Variance: 0.052
Range: 0.700
Distribution
Count: 10
Min: 24.600
Max: 25.300
| Bin | Range | Count | Freq | % |
|---|---|---|---|---|
| 1 | 24.60 - 24.72 | 2 | 0.200 | 20.0% |
| 2 | 24.72 - 24.83 | 2 | 0.200 | 20.0% |
| 3 | 24.83 - 24.95 | 1 | 0.100 | 10.0% |
| 4 | 24.95 - 25.07 | 1 | 0.100 | 10.0% |
| 5 | 25.07 - 25.18 | 2 | 0.200 | 20.0% |
| 6 | 25.18 - 25.30 | 2 | 0.200 | 20.0% |
📊 Distribution Analysis
Shape: Approximately symmetric (normal-like)
Sample Size: Small sample - collect more data for reliable analysis
Understanding histograms
A histogram is a graphical representation of the distribution of numerical data. It provides a visual interpretation of data by showing the frequency of occurrence of different value ranges in your dataset.
Histograms are essential for quality management because they help identify:
- Distribution patterns (normal, skewed, bimodal)
- Process centring and spread
- Outliers and unusual values
- Position relative to specification limits
- Data clustering and gaps
How to create and interpret histograms
- Collect your measurement data
- Determine the appropriate number of bins
- Calculate bin width and boundaries
- Count the frequency for each bin
- Plot the histogram and analyse the pattern
| Shape | What it suggests |
|---|---|
| Normal (bell-shaped) | Stable process with common-cause variation |
| Skewed right | Long tail to the right — check for delays or a natural lower bound |
| Skewed left | Long tail to the left — check for an upper limit or sorting |
| Bimodal | Two peaks — possibly mixed populations (two machines, shifts, or suppliers) |
| Uniform | Flat — drifting process or several overlapping distributions |
| Gaps / outliers | Missing data, measurement errors, or special causes |
Histogram applications in quality management
| Area | Typical uses |
|---|---|
| Process control | Monitor dimensional variation, check centring, spot drift, validate improvements |
| Statistical analysis | Assess normality, estimate capability, compare before/after data |
| Problem solving | Detect mixed populations, find measurement errors, verify corrective actions |
Worked example: machined shaft diameter
An illustrative study of 100 shafts with a specification of 25.0 mm ± 0.5 mm. The histogram looks close to normal, with a mean of 25.02 mm and a standard deviation of 0.18 mm.
(25.5 − 24.5) ÷ (6 × 0.18) = 0.93min(0.48, 0.52) ÷ (3 × 0.18) = 0.89A normal model predicts about 99.4% of parts within specification. But with Cp below 1.0 the spread is wider than the tolerance allows by the usual standards (Cp ≥ 1.33). Re-centring the 0.02 mm offset would barely move Cpk — the real work is reducing variation.