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Item stem and leaf plot

Definition

An item stem and leaf plot is a questionnaire display that places question identifiers at positions corresponding approximately to their average scores on a common response scale. It shows how item averages are distributed while preserving the identity of each question. In this usage, the labels represent questionnaire items, rather than the trailing digits of individual numerical observations.

What it means

A questionnaire can contain many statements rated using the same five-point response options. A list of averages tells you each item's result, but makes clusters harder to see. An item stem and leaf display groups or positions those averages visually and retains question numbers so the reader can return to the wording.
The plotted objects are items. A crowded part of the display means that several questions have similar average scores; it does not mean that many respondents selected that score. Confusing these two units changes the interpretation substantially.

How it works

Calculate each item's average using its valid responses and documented coding. Place its identifier near that average on the common scale. Where nearby labels overlap, stack them or group them into clearly explained intervals.
Keep a key linking identifiers to question text. Include response counts and clarify missing-data handling in an accompanying table. If higher scores are intended to have a consistent interpretation, check whether negatively worded items require reverse coding before comparison.
This is a descriptive summary. It does not establish that the response categories are equally spaced, that all questions measure one construct, or that small differences between means are meaningful.

Three practical examples

• An AI onboarding survey compares item averages for clarity, usability, and confidence while retaining question identifiers for follow-up discussion.
• A training coordinator scans several identically scaled workshop questions to locate items with unusually low average ratings.
• A service team displays item means alongside full response distributions so reviewers can distinguish a low average from disagreement among respondents.

Think of it this way

Imagine putting a numbered card for every question onto a ruler at its average score. Cards near the same point form a group. The card numbers tell you which questions are there; they are not pieces of the scores themselves.

Worked example

Consider an original questionnaire with six positively oriented items, Q1 through Q6, all coded from one to five. Higher numbers indicate a more favorable response. Initially, each item has five valid ratings.
Q1 receives 1, 2, 2, 3, and 2, totaling ten and averaging 2.0. Q2 receives 2, 3, 3, 4, and 3, totaling fifteen and averaging 3.0. Q3 receives 1, 1, 3, 5, and 5, also totaling fifteen and averaging 3.0.
Q4 receives 4, 4, 5, 4, and 5, totaling twenty-two and averaging 4.4. Q5 receives 3, 4, 4, 4, and 5, totaling twenty and averaging 4.0. Q6 receives 2, 2, 3, 2, and 3, totaling twelve and averaging 2.4.
On a display rounded to the nearest tenth, place Q1 at 2.0, Q6 at 2.4, Q2 and Q3 together at 3.0, Q5 at 4.0, and Q4 at 4.4. The two labels at 3.0 represent two questions, not two respondents.
For a coarser grouped version, intervals from 2.0 up to but excluding 3.0, from 3.0 up to but excluding 4.0, and from 4.0 through 5.0 each contain two item labels. State those boundaries explicitly so an item averaging exactly three is placed consistently.
Q2 and Q3 occupy the same mean position, but their responses differ sharply. Q2's ratings are concentrated around three. Q3 includes two ratings of one and two ratings of five. Their sample variances are respectively 0.5 and 4.0, calculated by dividing squared deviations from three by four.
The eightfold variance difference disappears in the mean-only display. Reviewing the response counts reveals the polarization that the shared average conceals. An item mean therefore cannot substitute for its underlying response distribution.
Now introduce Q7, worded negatively: 'The instructions were confusing.' Its raw ratings are 1, 2, 2, 1, and 4, averaging 2.0. If the intended display consistently shows favorability, reverse coding on the one-to-five scale uses six minus the original score. The recoded ratings are 5, 4, 4, 5, and 2, averaging 4.0.
Q7 consequently moves from the raw position 2.0 to the favorability position 4.0. This is a documented change of interpretation, not a change in respondents' answers. Keep the original wording and coding available.
For a separate missing-response illustration, suppose Q6 has only three valid ratings, 2, 2, and 3, with two responses missing. Its valid-response mean is 7/3, approximately 2.33. Coding the missing responses as zeros would instead produce 7/5 = 1.4, outside the intended treatment of missing answers and misleadingly lowering the mean.
Its displayed position might round to 2.3, but the underlying value and valid count of three should remain available. A label conveys an item identity and approximate location; it does not automatically communicate precision, sample size, or uncertainty.

Illustrative case study

Fictional company Birch Learning reviews feedback on an AI skills workshop. Its analyst uses item labels to identify questions near the low end of a common favorability scale, then opens the response distributions and wording for those items.
The review finds that one negatively worded question needs consistent reverse coding and that two equal means conceal different response patterns. The team corrects its presentation and investigates the questions individually. This fictional example demonstrates interpretation, not a reported improvement in training outcomes.

Common misconceptions and mistakes

The labels are question identifiers, not numeric leaves encoding the average.
The distribution shown is across item means, not across all respondent ratings.
Equal means do not imply equal response patterns.
Missing responses are not automatically zero or neutral.
Common response options do not prove that items measure the same underlying concept.

Business use

Use this display as a compact navigation aid for questionnaire review. Pair it with question text, coding direction, valid counts, and response distributions. Let it guide investigation rather than serve as a standalone ranking of priorities or proof that one question's result differs reliably from another's.

People also ask

Is it an ordinary stem-and-leaf plot?

No; this questionnaire variant uses item labels.

Can two questions occupy one position?

Yes.

Does a low mean explain the problem?

No; examine wording, responses, and context.

Check your understanding

What do Q2 and Q3 at 3.0 represent?

Answer: Two item averages.

Which has greater sample variance?

Answer: Q3.

What is Q7's reverse-coded mean?

Answer: Four.

Related terms

• Likert scale
• Missing data
• Dot plot
• Stem and leaf plot
• Questionnaire item
• item mean
• reverse coding
• response distribution

Learn next

Compare item-average displays with stacked response charts, then study ordinal measurement and uncertainty in questionnaire summaries.

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Sources

NIST/SEMATECH, e-Handbook glossary, item stem and leaf plot and Likert scale: https://www.itl.nist.gov/div898/handbook/glossary.htm . All ratings, calculations, presentation choices, and company details are original illustrations.

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