Boxplot

Anatomy of a Boxplot

A boxplot summarizes a distribution in one compact graphic. All elements are derived from the sorted observations and show location, spread, skewness, and outliers at a glance.

Box: The rectangle spans from the 1st quartile (Q1, 25 % point) to the 3rd quartile (Q3, 75 % point). It contains the middle 50 % of the data. Its length is the interquartile range (IQR = Q3 − Q1) and is the most robust measure of spread in the boxplot.

Median Line: The line crossing the box marks the median (Q2, 50 % point) — the value with half the data above and half below. If the line sits centered in the box, the distribution is symmetric; if it is shifted, the distribution is skewed.

Mean Marker: A diamond (or cross) marks the arithmetic mean. When mean and median sit close together, the distribution is roughly symmetric. A noticeable gap indicates skewness or the influence of outliers.

Whiskers: The two lines extending from the box are called whiskers. They reach to the smallest/largest observation that still lies within 1.5 × IQR of the box — not simply to the overall minimum or maximum. They mark the range of "normal" variation.

Fences (inner limits): The invisible cutoffs at Q1 − 1.5 × IQR and Q3 + 1.5 × IQR are called fences. They are not specification limits but a purely statistical rule of thumb (Tukey) separating outliers from "normal" values.

Outliers: Individual points beyond the whiskers are drawn as separate markers. They lie outside the Tukey fences and should always be investigated — not every outlier is an error; sometimes the most important information sits in exactly these points.

In short: box = middle 50 %, median line = location, whiskers = normal range of variation, points beyond = outliers. With these four building blocks you can quickly characterize any distribution and compare several groups side by side.

Methodology

A boxplot (box-and-whisker plot) is a graphical display of a dataset's distribution based on its five-number summary: minimum, first quartile (Q1), median, third quartile (Q3), and maximum.

Box (IQR): The box spans from Q1 to Q3, containing the middle 50 % of the data. Its width is the interquartile range (IQR = Q3 − Q1).

Whiskers: Whiskers extend to the smallest/largest value within 1.5 × IQR of Q1/Q3. Values beyond are plotted as outliers.

Median Line: The vertical line inside the box marks the median (50th percentile). Its position relative to the box indicates skewness.

Mean Diamond: The diamond marks the arithmetic mean. Deviation from the median suggests skewness or outlier influence.

Input Modes

• Multiple columns: Each selected numeric column produces one boxplot. Ideal for comparing different measurements.
• Grouped: A single value column is split by a grouping column (categorical attribute, e.g. machine, shift, supplier). Ideal for comparing the same measurement across categories.

Practical Example

1. Open the Boxplot module.
2. Set input mode to "Grouped".
3. Select value column = "Wall Thickness", grouping column = "Shift".
4. Click "Create Boxplot".
5. Result: Three horizontal boxplots stacked vertically — one per shift.
6. Compare: Night shift shows a wider box (more variation) and two low outliers.

Interpretation

What to look for

• Median position in the box: Centered → symmetric, off-center → skewed.
• Box width (IQR): Narrow → low spread, wide → high spread.
• Whisker length: Asymmetric whiskers indicate skewness.
• Outliers: Individual points beyond whiskers. Investigate causes (measurement error, special events).
• Mean vs. Median: Large gap → outliers are pulling the mean.
• Comparing multiple boxplots: Non-overlapping boxes suggest potentially significant differences.

Pitfalls

Examples

This module ships with the following example datasets — load any of them in the app with a single click.