Histogram Generator
Create interactive histograms for data distribution analysis, identify patterns, and perform statistical quality control
Histogram Generator
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)
Process Capability Hint: High variation - consider process improvement
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 centering and spread
- Outliers and unusual values
- Process capability and specification limits
- Data clustering and gaps
How to Create and Interpret Histograms
Creating a Histogram:
- 1Collect your measurement data
- 2Determine the appropriate number of bins
- 3Calculate bin width and boundaries
- 4Count frequency for each bin
- 5Plot the histogram and analyze patterns
Interpretation Guidelines:
- • Normal Distribution: Bell-shaped, process is stable
- • Skewed Right: Long tail to the right, check for delays
- • Skewed Left: Long tail to the left, check for limits
- • Bimodal: Two peaks, possible mixed populations
- • Uniform: Flat distribution, random variation
- • Gaps/Outliers: Missing data or special causes
Histogram Applications in Quality Management
Process Control
- • Monitor dimensional variations
- • Check process centering
- • Identify process drift
- • Validate process improvements
Statistical Analysis
- • Test for normality
- • Calculate process capability
- • Estimate population parameters
- • Compare before/after data
Problem Solving
- • Identify root causes
- • Detect mixed populations
- • Find measurement errors
- • Validate corrective actions
Real-World Example: Manufacturing Shaft Diameter
Scenario: Machined Shaft Quality Control
A manufacturing plant measures shaft diameters (target: 25.0mm ± 0.5mm) from 100 parts:
Sample Data Analysis:
- • Mean: 25.02mm (slightly off-center)
- • Standard deviation: 0.18mm
- • Distribution: Nearly normal
- • Range: 24.6mm to 25.4mm
- • Outliers: 2 parts > 25.3mm
Quality Insights:
- • Process is slightly off-center (+0.02mm)
- • Good process capability (Cp ≈ 0.93)
- • 98% of parts within specifications
- • Investigate outliers for special causes
Action: Adjust machine offset by -0.02mm and investigate outlier causes. Result: 100% parts in specification.
Frequently Asked Questions
How many bins should I use for my histogram?
A good rule of thumb is to use 5-20 bins depending on your data size. For small datasets (<50 points), use 5-10 bins. For larger datasets (>100 points), use 10-20 bins. You can also use Sturges’ rule: bins = 1 + 3.322 × log(n).
What’s the difference between a histogram and a bar chart?
Histograms show continuous data distribution with adjacent bars representing ranges of values. Bar charts show discrete categories with gaps between bars. Histograms are for numerical analysis, bar charts are for categorical comparison.
How do I know if my data is normally distributed?
Look for a bell-shaped, symmetric distribution in your histogram. Most data should cluster around the center with fewer points at the extremes. For formal testing, use statistical tests like Shapiro-Wilk or Anderson-Darling.