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 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 |
| Are the values developing over the measurement series? | Line chart |
| Do the data follow a normal distribution? | Q-Q-Plot |
| How do several groups compare? | Boxplot (multiple groups side by side) |
Advantages of graphical analysis
- Quick overview: Grasp distribution properties 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 metrics (e.g., mean, standard deviation, Cm/Cmk, Cp/Cpk).
Diagram Types
Boxplot (Box-Whisker-Plot)
The boxplot is one of the most important tools of exploratory data analysis. It presents the distribution of a dataset compactly and shows the central tendency, the spread, and any potential outliers.
Structure of a boxplot
| Element | Description | Statistical Value |
|---|---|---|
| Center line (Median) | Horizontal line in the box | 50th percentile (Q2); divides the data into two equal halves |
| Lower box edge | Bottom edge of the box | 25th percentile (Q1); 25% of the data lies below it |
| Upper box edge | Top edge of the box | 75th percentile (Q3); 75% of the data lies below it |
| 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 of Q1 - 1.5 * IQR or Q3 + 1.5 * IQR |
Interpretation
Tip: Pay attention to the following points when viewing the boxplot:
- Symmetry: If the median is centered in the box, it indicates a symmetric distribution
- Box width: A narrow box indicates low spread, a wide box indicates high spread
- 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 limit (e.g., roughness values) |
| Left-skewed boxplot | Median near Q3, lower whisker longer | Natural upper limit, saturation effects |
| Many outliers (top) | Numerous points above the upper whisker | Occasional disturbances, wear |
| Very narrow box | Q1 and Q3 lie close together | Very low spread; high process capability |
Comparative boxplots
A particularly valuable application is the comparison of multiple groups side by side, e.g.:
- Comparison of different machines
- Comparison of different shifts or operators
- Comparison of different material batches
- Before-and-after comparison following a process improvement
Histogram
The histogram shows the frequency distribution of the 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 | Optional displayable 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 produce a restless image. my8data automatically selects the number of classes according to the 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 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 problems in measurement |
| Rectangular (uniform) | All bars approximately equal height | Uniform distribution; no clear process mean |
Line Chart (Linechart)
The line chart displays the measured values in their acquisition order. Each point corresponds to a measurement; the connecting line makes temporal developments visible.
Application examples
- Recognize trends (e.g., tool wear over time)
- Identify jumps or level changes following interventions or batch changes
- Identify outliers within the measurement series
Warning: The line chart shows only the temporal sequence, not statistical control limits. For a formal stability assessment, use the SPC control charts.
Q-Q-Plot (Normal Distribution Test)
In the Q-Q-Plot (Quantile-Quantile diagram), the observed measured values are plotted against the theoretical quantiles of the normal distribution. If the points lie close to the reference line (within the confidence band), this suggests a normal distribution.
Interpretation
| Pattern | Description | Meaning |
|---|---|---|
| Points on the reference line | Data follow the normal distribution | Distribution assumption met |
| S-shaped deviation | Tails heavier/lighter than normal | Deviation in kurtosis |
| Arc-shaped deviation | Distribution is skewed | Skewness (e.g., natural limit) |
| Points outside the band at the ends | Outliers or heavy tails | Check distribution assumption |
Tip: The Q-Q-Plot complements the histogram: While the histogram shows the shape, the Q-Q-Plot makes deviations from the normal distribution — especially in the boundary areas — clearly visible.
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 the PNG export for quick reports and the SVG export when you want to further process the graphics in your own reporting tool.