# VectorPaint equal-bin histograms: assign boundary values before drawing counts
Language: en
Canonical: [VectorPaint equal-bin histograms: assign boundary values before drawing counts]()
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Published: 2026-11-06T00:00:00+08:00
Modified: 2026-11-06T12:13:22+08:00
Author: Bison
Bin eight invented values into three equal intervals, checking single assignment at boundaries, total counts and neighbouring bar widths.
English translation of the [Chinese original](), translated on 2026-11-06. Original publication dates, attribution, code and version notes are retained.
A histogram’s horizontal position represents numerical intervals rather than arbitrary categories. Manually assign eight invented numbers to three bins and draw frequencies with equal-width rectangles. Keep binning and counts in a personal list; no built-in statistics or chart generation is assumed, and readable graphics give invented data no real survey significance.
## Fix eight values and three bin boundaries
Create a 1200 by 800 pixel canvas and externally list 0,1,2,2,3,4,5,6. The duplicate 2 represents two observations, not a duplicate to delete. Use fictional x quantities and three width-2 bins: 0–2,2–4,4–6. Record eight samples and invented provenance without borrowing an institution’s credibility. The y axis is frequency, not value or percentage. Preserve source order for checking; sorting must not merge the two 2s. Establish identity and bins before graphics.
## State inclusion rules explicitly
Make the first two bins left-inclusive/right-exclusive and the last inclusive at both ends to include 6. Thus 0,1 enter bin one; both 2s and 3 bin two; 4,5,6 bin three, giving 2,3,3. Boundary values 2 and 4 are counted once. A missing 6 calls for checking the final rule, not forcing bar height. Explain intervals in words rather than assuming conventions. This is the exercise definition, not a universal software default; new boundaries need new explanations.
## Position interval width and frequency on separate axes
Space x=0,2,4,6 equally and let each bar occupy its complete interval, adjoining rather than separated by large categorical-chart gaps. Use y=0–4 with equal frequency steps and heights 2,3,3. Establish axes/labels before bars rather than treating source values as three category names. All bars start at frequency zero; counts determine height and bins determine width. Hand-drawn references remain artwork; native-grid/guide output needs separate checks rather than being assumed frequency boundaries.
## Check individual assignments and total frequency
Assign each observation individually, then check 2+3+3=8. A correct total is necessary but two wrong assignments can cancel, so retrace every item. Temporary IDs distinguish the two observations valued 2 without changing their identical value. An empty bin would retain its zero-frequency position, not disappear from the axis. All bins here are occupied; do not move samples to make heights more even. Layout preference does not determine a distribution.
## Change one value to inspect a boundary transition
In a copy, change the original 1 to 2. Sample size remains eight and frequencies become 1,4,3. Update source/list before both affected heights; y maximum 4 still fits. Increasing the second without decreasing the first is wrong. Keep boundaries fixed instead of silently rebinning to preserve old heights. Name original/test separately and keep numbers and drawing at one revision. Rectangles do not follow data automatically; the test identifies manually maintained graphics and explanations.
## Do not reuse the same height interpretation for unequal bins
Equal widths here permit direct frequency-height comparison. A later unequal-width design needs reconsidered statistical encoding and scale rather than silently preserving the same area/frequency interpretation. This provides no automatic density calculation or reliable probability estimate from eight observations. Title it an eight-value fictional equal-bin frequency exercise. Real data needs scope, units and reuse permission before bin choice; changing a few labels in the finished image does not produce a complete analysis.
## Audit exported axes, bins and counts in order
Save source data and editable rectangles. In export, read axes/intervals before 2,3,3 and total eight. At small size, doubled boundary strokes must not resemble an extra narrow bin; remove actual duplicates. Keep labels off tops and zero baseline clear. Test backgrounds rather than assuming white objects disappear. Include bin definition, dataset revision and dimensions in filenames and exclude changed-value tests. Retain the source list because a raster image is not traceable data; it expresses this assignment of eight items into three bins.
## Return to individual assignments when totals hide errors
For three items in bin one, check whether 2 was wrongly included; a missing last-bin item may be 6 excluded. Equal bar widths with unequal x spacing call for axis repair, not label edits. Large gaps need interval occupancy checks instead of categorical-card layout. Even with total eight, reread every observation, then recheck heights and interval rules. Meaning comes from assignments, sample count and bar provenance, not rectangles whose heights happen to sum to eight.
## Related tutorials and sources
[VectorPaint bar chart: keep lengths, numbers and units consistent](), [VectorPaint scatterplots: map every point to two values]().
Sources checked on November 6, 2026: VectorPaint 1.0.8, requiring iOS / iPadOS 17.0 or later. Capability scope follows the [official App Store description]() and [Apple public version lookup](). These are exercises and checks you can perform, without a claim of step-by-step physical-device testing or verification in every target environment. Example content is instructional; follow the controls in your installed version.