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Math Details

Under review — candidate for removal

A dot plot performs no statistical inference; its "math" is the dot-binning and layout geometry used to render the plot. This page is flagged for review — it may be removed if that rendering detail is judged out of scope for a Math Details page.

This page gives the formulas Quantum XL uses to bin and stack the dots when drawing a dot plot.

Notation

Term	Description
\(n\)	number of data points
\(x_{\min}, x_{\max}\)	smallest and largest data values

Dot (bin) width

Quantum XL uses Wilkinson's dot-density rule to choose the bin width, scaled to keep the plot within its available width:

\[ \text{dotSize} = \frac{0.25}{\sqrt{n}}\cdot m \]

where \(m\) is a scale multiplier increased iteratively until the plot fits its width budget.

Bin assignment

Points are grouped left to right: a value joins the current bin while

\[ x - x_{\text{binStart}} \le \text{interval} \]

otherwise it opens a new bin. Each bin's count is the number of (frequency-weighted) points it captures.

Stacking and plot height

\[ \text{stackHeight} = \left\lceil \frac{\text{binCount}}{\text{obsPerDot}} \right\rceil, \qquad \text{plotHeight} = \text{markerSize}\cdot 1.4\cdot(\text{maxStack} + 1) \]

Term	Description
obsPerDot	observations represented by one dot; increased (\(1, 2, 5, 10, 20, \dots\)) so the plot fits within the row budget
maxStack	the tallest bin's stack height

References

• Wilkinson, L. (1999). Dot plots. The American Statistician, 53(3), 276–281.