VectorPaint stem-and-leaf displays: preserve tens, units and repeated values

English translation of the Chinese original, translated on 2026-11-08. Original publication dates, attribution, code and version notes are retained.

A stem-and-leaf display is not an arbitrary split into two columns. Readers need the place-value key, and repeated leaves represent repeated observations. Manually arrange eight invented integers and reconstruct the original list from the display. This checks low-risk data representation, uses no real personal records and assumes no automatic grouping, distribution calculation or statistical inference.

Fix the eight observations and their unit

Record 12,14,14,19,20,23,27,30 externally, defining the unit as fictional practice points rather than real exam scores. Preserve all eight in ascending order; the repeated 14 is not a duplicate record to clean away. Reserve five regions on a new canvas: title, stem column, divider, leaf column and key. Keep the original list externally or on a separate checking layer rather than crowding every original number into the final display. The goal is reconstruction of eight observations, not merely three tidy rows.

Write the key before splitting values

Define stems as tens and leaves as units. Write a key such as “1 | 2 means 12 fictional practice points”. The vertical bar separates fields; it is neither division nor an absolute-value sign. Deliver the key with the display rather than expecting readers to guess 120 or 1.2. Test 12 as stem 1, leaf 2, and 30 as stem 3, leaf 0. A zero leaf is a valid units digit, not an empty row. Check these two examples before entering all leaves.

Place three rows while retaining repetition

For stem 1, place leaves 2,4,4,9 left to right; for stem 2, place 0,3,7; for stem 3, place 0. Each leaf is one digit with a clear consistent gap, not a combined four-digit number 2449. Both leaves for 14 must remain. Temporary colours or pale marks may assist counting, but independent leaf positions must identify them in the final. With editable text, remember that glyph widths and spaces may differ. Place individual digits and inspect alignment if necessary rather than promising that repeated spaces create a precise table.

Reconstruct the original list leaf by leaf

Without looking at the source list, read stem 1 as 12,14,14,19, stem 2 as 20,23,27 and stem 3 as 30. Write this reconstruction separately and pair it with the original eight values, checking both order and multiplicity. Four plus three plus one leaves equals eight observations; three stems do not mean three observations. For a total of seven, check the repeated 14 first. If 3 appears, check whether the stem for 30 was treated as a whole value. This is manual completeness checking, not automatic app comparison or correction.

Change only the relevant row when adding 21

Duplicate the display and add 21 to the source list, increasing observations from eight to nine. Stem 2 becomes 0,1,3,7; stems 1 and 3 remain unchanged. Insert the new leaf between 0 and 3 rather than appending it at the right while claiming ascending order. Adjust that row’s spacing, then inspect unintended movement elsewhere. Label the versions eight and nine observations, using one change marker rather than recolouring every leaf. Preserve the original so frequency changes remain attributable to the new value rather than recoding.

Do not mix incompatible keys in one display

Do not silently remove decimal points from another dataset while retaining this key. Define its unit and splitting rule separately or use another display, preserving original precision. This exercise does not extend to negative values or split stems. Horizontal leaf spacing is layout, not a continuous distance scale beginning at the stem. Widening four leaves gives no area interpretation to the difference between 19 and 12. Restrict claims to these eight observations and the added value rather than treating this drawing exercise as a universally suitable statistical method.

Read each digit and the key in the exported output

Save the editable source and export a viewing-size PNG. Open it independently and read everything from title to key. Inspect a divider touching digits, ambiguous zero versus letter O and two overlapping 4s. At small size, increase text size or simplify decoration rather than deleting repeated observations. Hide pale checking marks if they are not part of delivery: ordinary objects do not stop exporting merely because they serve inspection. The original output must still reconstruct eight values without the list, and the revision nine.

Troubleshoot count, key and order separately

For mismatches, count leaves, inspect the key and then check within-row order; do not alter the source list to match the drawing. A missing 14 points to repetition, 30 becoming 3 to the zero leaf, and a trailing 21 to sorting. If all digits are correct but units unclear, repair title/key rather than concealing the issue with colour legends. Preserve the source, reconstructed list and revision differences, each traceable to a position in the display. This establishes readable encoding, not real score analysis, anomaly detection or automatic statistics acceptance.