Statistical Methods
Recover histogram heights from unequal-width bins
Define the task
A table of counts by interval can support a histogram if the numeric edges and denominator survive the export. Record the unit and edges before drawing rectangles. Check that bins cover the intended range with no gaps or overlaps. Keep overflow and missing counts visible until the normalization population is defined.
Carry out the check
Divide each count by the total included count to get its probability mass. Divide that mass again by the bin width to get density. Label the vertical axis with reciprocal units. To check a published figure, multiply each height by its width and add the areas. They should sum to one, apart from rounding. Bar height alone answers a different question when widths differ.
Worked hypothetical example
For hypothetical bins spanning 0–1 and 1–4 minutes with 20 observations in each, both rectangles need area 0.5. Their heights are 0.5 and about 0.1667 per minute. Drawing them equally tall would give the second rectangle three times the area of the first. Existing bin totals cannot recover the distribution inside a bin.
Method checked 10 November 2026 against R documentation: Histograms.