Boxplot and Statistical Diagrams
Overview
The Boxplot and Statistical Diagrams module in my8data provides you with powerful visualization tools to graphically prepare and analyze your measurement data. Visual representations make distributions, outliers, and relationships recognizable at a glance and complement the numerical analysis results of the other modules.
When do you use this module?
| Question | Suitable Diagram Type |
|---|---|
| How are the measured values distributed? Are there outliers? | Boxplot |
| What does the frequency distribution look like? | Histogram |
| Is there a relationship between two characteristics? | Scatter Plot |
| How do multiple groups compare? | Boxplot (multiple groups side by side) |
Advantages of graphical analysis
- Quick overview: Capture distribution characteristics at a glance
- Outlier detection: Unusual values become immediately visible
- Comparability: Multiple datasets or groups can be directly compared
- Communication: Diagrams facilitate conveying statistical findings to non-statisticians
Info: Graphical analyses do not replace numerical evaluation, but rather complement it. Always use diagrams in combination with calculated key values (e.g., mean, standard deviation, Cm/Cmk, Cp/Cpk).
Diagram Types
Boxplot (Box-Whisker Plot)
The boxplot is one of the most important tools in exploratory data analysis. It compactly represents the distribution of a dataset and shows central tendency, dispersion, and any outliers.
Structure of a Boxplot
| Element | Description | Statistical Value |
|---|---|---|
| Middle line (Median) | Horizontal line in the box | 50th percentile (Q2); divides the data into two equal halves |
| Lower box edge | Lower edge of the box | 25th percentile (Q1); 25% of the data lie below this |
| Upper box edge | Upper edge of the box | 75th percentile (Q3); 75% of the data lie below this |
| Box (IQR) | Area between Q1 and Q3 | Interquartile range (IQR = Q3 - Q1); contains the middle 50% of the data |
| Lower whisker | Line below the box | Smallest value within Q1 - 1.5 * IQR |
| Upper whisker | Line above the box | Largest value within Q3 + 1.5 * IQR |
| Outliers | Individual points beyond the whiskers | Values outside Q1 - 1.5 * IQR or Q3 + 1.5 * IQR |
Interpretation
Tip: When looking at a boxplot, pay attention to the following points:
- Symmetry: If the median is centered in the box, this indicates a symmetric distribution
- Box width: A narrow box shows low dispersion, a wide box shows high dispersion
- Whisker length: Asymmetric whiskers indicate a skewed distribution
- Outliers: Individual points beyond the whiskers require special attention
Typical distribution patterns in the boxplot
| Pattern | Description | Possible Cause |
|---|---|---|
| Symmetric boxplot | Median centered, whiskers equal length | Normally distributed data; stable process |
| Right-skewed boxplot | Median near Q1, upper whisker longer | Natural lower bound (e.g., roughness values) |
| Left-skewed boxplot | Median near Q3, lower whisker longer | Natural upper bound, saturation effects |
| Many outliers (above) | Numerous points above the upper whisker | Occasional disturbances, wear |
| Very narrow box | Q1 and Q3 lie close together | Very low dispersion; high process capability |
Comparative Boxplots
A particularly valuable application is the comparison of multiple groups side by side, for example:
- Comparison of different machines
- Comparison of different shifts or operators
- Comparison of different material batches
- Before-and-after comparison after a process improvement
Histogram
The histogram shows the frequency distribution of measured values. The measured values are divided into classes (bins), and the height of each bar corresponds to the number of measured values in that class.
Elements of the Histogram
| Element | Description |
|---|---|
| Bar | Height corresponds to the frequency of values in the respective class |
| Class width | Width of each bar; is calculated automatically or can be set manually |
| Normal distribution curve | Optionally displayed theoretical distribution |
| Specification limits | Vertical lines at USL and LSL (if defined) |
Tip: The number of classes significantly influences the appearance of the histogram. Too few classes hide details, too many classes create a restless image. my8data automatically selects the number of classes according to Sturges' or Freedman-Diaconis' rule, but you can also adjust the number manually.
Interpretation of typical histogram shapes
| Shape | Description | Possible Cause |
|---|---|---|
| Bell-shaped | Symmetric, one peak | Normally distributed data; stable process |
| Bimodal (two-peaked) | Two peaks | Mixture of two populations (e.g., two tools) |
| Truncated | Sharp drop-off on one side | 100% inspection removes parts beyond a limit |
| Comb-shaped | Alternating high and low bars | Rounding issues in measurement |
| Rectangular (uniform) | All bars approximately equal height | Uniform distribution; no clear process mean |
Scatter Plot
The scatter plot graphically represents the relationship between two characteristics. Each point corresponds to a measurement pair (x, y).
Application Examples
- Correlation between two measured values (e.g., diameter and roundness)
- Influence of a process parameter on a quality characteristic (e.g., temperature and dimensional accuracy)
- Measurement comparison between two measuring instruments or measurement methods
Interpretation
| Pattern | Description | Correlation | ||
|---|---|---|---|---|
| Points rise from left to right | Positive correlation | r > 0 | ||
| Points fall from left to right | Negative correlation | r < 0 | ||
| Points form a cloud without direction | No correlation | r ≈ 0 | ||
| Points lie close to a straight line | Strong correlation | r | > 0.8 |
Warning: A correlation between two characteristics does not automatically mean that one characteristic causes the other (correlation is not equal to causality). Always interpret relationships in the context of your process knowledge.
Export Diagrams
All diagrams created in my8data can be exported in various formats:
- PNG: For presentations and reports
- PDF: For print-ready documents
- SVG: For scalable vector graphics
Tip: Use PNG export for quick reports and SVG export when you want to further edit the graphics in your own reporting tool.