How this calculator works
Each observation becomes a dot. Repeated values stack vertically at the same horizontal position, so their stack height is their frequency. The coordinate table gives x and stack height for drawing; the frequency table helps compare clusters. Values that differ by even a small amount remain separate. Round data beforehand only when the measurement precision justifies it.
Formula
f(x) = number of observations equal to x; relative frequency = f(x)/n; stack heights = 1,...,f(x).
Worked example
The data 1, 1, 2, 4, 4, 4 produce stacks of heights 2, 1 and 3 at x = 1, 2 and 4. There are six dots in total.
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Frequently asked questions
Are the y coordinates measurements?
No. Stack height counts repetitions; x holds the observed measurement.
Does the tool group nearby values?
No. It uses exact entered values, without bins or a tolerance.
Where is the chart?
The tables provide the stacks and individual dot coordinates for drawing a chart.