Three fixed rounds show mean 8 and median 4 for the original list, mean 5 and median 4 after the replacement, then mean 6 and median 5 for an even four-card list. Sorting and round controls keep the observation count, card identities and calculations together. Check requires both numeric answers. The separate teacher disclosure can reveal the reference arithmetic while answers are blank.
Separate a total from an ordered position
OpenStax defines mean through total divided by count, and median through the middle of ordered data. With an odd count, use the middle value; with an even count, average the two middle values. The position of a card and its numeric value are different information.
The fictional original cards are C01 = 2, C02 = 4, C03 = 4, C04 = 6 and C05 = 24. There are five observations, including two separate cards valued 4. Do not deduplicate them. Sorting changes their order, not their count or values. Each card labels its ID and current display position. The reference names the numerically sorted values and their middle positions, so a shuffled display cannot turn a position label into the median.
Work the original round
Round S1 sorts to 2, 4, 4, 6, 24. Add the values to get 40 and divide by 5 for mean 8. The third position is in the middle, and its value is 4, giving median 4. The two 4 cards occupy different positions while both contribute to the total.
Before checking, ask learners to enter a mean, a median and a reason. The sort control makes the ordered list inspectable without marking the round complete. Blank values stay unanswered rather than becoming zeros. The teacher key sits behind a deliberate reveal; it is not copied into the learner's fields.
Replace one value without adding an observation
In S2, replace C05's 24 with 9 and retain S1 for comparison. The revised list is 2, 4, 4, 6, 9, with sum 25 and count 5. Mean 25 ÷ 5 = 5; the third value is still 4, so median 4. The sum has dropped 15, and 15 ÷ 5 explains the mean's decrease of 3.
The median stays 4 for this replacement because the middle ordered value remains 4. That is not a claim that medians never change or are always preferable. Call 24 the largest original value rather than an outlier unless you supply an outlier criterion. Neither list represents a population or actual student measurements.
Handle the even round explicitly
S3 is a separate dataset E01 = 2, E02 = 4, E03 = 6 and E04 = 12. The sum is 24, count 4 and mean 6. Its middle positions are second and third, holding 4 and 6. Median (4 + 6) ÷ 2 = 5. Five need not appear on a card; calculating a median does not create another observation.
Ask the learner to identify both middle values before computing. Choosing just 4 or 6 uses only one of the two central positions. Averaging every value gives the mean instead. The local feedback points to these calculations for the fixed round, while the learner's explanation remains for teacher review.
Keep the linked displays consistent
Switching to S2 updates its cards, sum, count and key together; it must not leave S1's 40 or mean 8 beside the revised list. Each of the three rounds retains its own attempt. Editing an answer removes stale feedback, and repeated checks do not create additional rounds.
Reset restores the original ordering and clears predictions, answers, reasoning and revealed feedback. The page's temporary entries are not saved learner work. Keep the blank calculation sheets and separate key in the teaching packet, and use the arithmetic contrast to prompt explanations rather than treating a matched answer as broad statistical understanding.
Copy this prompt
Create a complete original HTML example in US English for this task: Statistics games for the classroom. Return one self-contained HTML file. Include all styles, data and JavaScript in the file. Use no remote dependencies. Return the working page, not an outline.
S1 cards C01 = 2, C02 = 4, C03 = 4, C04 = 6, C05 = 24: sum 40, count 5, mean 8, median 4 at position 3. S2 replaces only C05 with 9: sum 25, count 5, mean 5, median 4, mean change-3. S3 separate E01 = 2, E02 = 4, E03 = 6, E04 = 12: sum 24, count 4, mean 6, median (4 + 6)/2 = 5. Preserve both 4 cards and original S1.
Create labeled original count cards with IDs and current Display position labels, fixed S1/S2/S3 buttons, a numeric Sort button and equivalent ordered-list text. Start S1/S2 in C05,C02,C01,C04,C03 order; start S3 in E04,E01,E03,E02 order. Display count and sum, with center calculations revealed only by an attempt check or teacher-key action. Checked feedback and the teacher key must explicitly list the numerically sorted values and identify sorted middle positions, even before Sort changes the displayed cards. Provide an initially blank prediction field about replacing 24 with 9, separate from the later explanation. Blank learner mean/median/reason fields initially; check fixed numeric answers with arithmetic explanation, not prose grading. Replacement must update every linked display and preserve 5 observations. Give S3 both middle positions. Each round retains its own attempt, edits clear feedback, repeat checks add no item count, reset clears the prediction and answers and restores original ordering. No arbitrary-data parser, inference, outlier label, grading service or persistence.
Use a page design suited to this particular task, readable text at least 16 px, generous spacing, visible keyboard focus and explicit labels. At 360 px, stack the content without page-level horizontal scrolling. Use type="button" click handlers for actions. Keep source facts and sample results distinct from actual observations. Leave unknown details visible rather than inventing them. Controls update only this temporary page; distinguish local changes from actual records. Provide concise task-specific feedback and a reset that clears entered answers and stale results.
Explain the change of three
Put the S1 and S2 ordered lists next to each other. For a teaching discussion, render the HTML lists and arithmetic in NOS so a colleague can inspect the same removed value and unchanged middle position. Ask why removing 15 from the sum lowers the mean by 3 while position 3 still holds 4. Follow with S3: ask which two positions determine its median and why the answer 5 needs no fifth card.