Show when changing one data point affects the mean and median differently

An annotated series of single-change examples showing when the mean and median diverge or agree.

Choose one of three approaches. The steps for that option appear below.

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Gemini: drafts the table and works out the numbers

Gemini drafts the case table, works out each mean and median and drafts annotations. You check and decide.

  1. You

    Get ready

  2. Gemini

    Draft case table

  3. You

    Check the table

  4. Gemini

    Compute and annotate

  5. You

    Recompute and decide

  1. Have ready: definitions, range, baseline, prediction

    Use: You

    Course definitions, permitted range, baseline dataset and the learner prediction.

    Check

    Check every dataset is labelled constructed, not observed.

  2. Draft the controlled case table

    Use: Gemini

    Ask Gemini to draft the case table from your definitions, range and baseline: one declared observation changed per case, every dataset labelled constructed.

    Details

    What to paste into the tool

    Using only the supplied definitions, permitted range and baseline, draft a controlled case table where each case changes exactly one declared observation from the previous case. Preserve case IDs. Label every dataset as constructed, not observed. Do not generate learner evidence. Show which values you used.

  3. Check the case table against the definitions

    Use: You

    Check the table against the definitions, range and baseline. Fix or reject any case that breaks the one-change condition.

    Check

    Do not assume the drafted table meets the teaching constraints. Check ordering, range and the one-change condition. Store the withheld case key separately, not in the learner-facing table.

  4. Work out mean and median, draft annotations

    Use: Gemini

    Import the checked table. Ask for each case mean and median in separate columns, then annotations and unrevealed prediction prompts.

    Details

    What to paste into the tool

    For each case ID compute the arithmetic mean and median of only the supplied observations. Preserve case IDs. Do not generate new observations or learner evidence. Show which values you used. For each case, write a short annotation from the supplied course definitions explaining what the changed observation did to the mean and the median. Draft one prediction prompt per case for the learner. Keep the withheld case's solution out of the learner-facing output. Mark anything the definitions do not settle instead of guessing.

  5. Recompute, check annotations and decide

    Use: You

    Recompute each mean and median, check annotations against the definitions and check the withheld key stayed separate.

    Check

    Do not assume sampled context covers the table; recompute every result independently. Do not reveal the key until prediction, and check the withheld-case prompt does not reveal its answer. Make no claim of learner mastery.

Before you paste into any AI tool, remove any confidential information. Put it back at the end.

Tools in this workflow

Deciding between Claude and Gemini for this? See the comparison.

Final check

Tutor verifies baseline ordering, range constraints and that only one observation changes per case before any calculation is relied on.

Tutor independently recomputes both summaries and verifies the withheld-case prompt does not reveal its answer; the withheld key stays separate.

All illustrative datasets are labelled constructed, not observed evidence.

The draft includes an unrevealed prediction prompt and no claim of learner mastery. Preparation only. The named human reviews the result; do not submit learner work, publish material, alter official grades or make placement decisions automatically.

Check the result against your original inputs. Approve it before sharing or acting.

What still needs checking
  • No cited evidence confirms the correctness of any drafted explanation; all explanations are checked against the course definitions by the tutor.

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