A scatterplot needs intact pairs, not separately sorted columns

Abstract

Educational reading copy of the activity first published by Figran Team at https://figran.mataroa.blog/blog/a-scatterplot-needs-intact-pairs-not-separately-sorted-columns/. This directory version retains the exercise, fictional values and answers; it removes the commercial website link. No Figran account or purchase is needed. By Figran Team. We are associated with Figran, a commercial AI-assisted visual creation service. This teaching activity was prepared with AI assistance and checked for internal arithmetic consistency. All card IDs and dot counts below are invented for this exercise. They are not research measurements, classroom results, or evidence about a product's performance. The activity can be completed on paper without a software account or purchase. A scatterplot places each complete observation at a pair of coordinates. Two columns that contain the right individual values can still supply the wrong pairs. This activity asks learners to trace every plotted point back to the record that supplies both coordinates, rather than judging a table by its neatness or by its column totals. 1. Define the pair before moving any values Each fictional card has a count of blue dots and a count of orange dots. The words "blue" and "orange" name two different fields; their names are written out, so colour perception is not needed to distinguish them. Let x mean the blue-dot count and y mean the orange-dot count on the same card. Use this five-card source version throughout Tasks 1 to 4 and Task 7: Source row; Card ID; Blue dots, x; Orange dots, y 1; A; 1; 8 2; B; 2; 3 3; C; 3; 5 4; D; 4; 1 5; E; 5; 7 The first card supplies (1, 8), not an x value that may be freely combined with another card's y value. Card ID is the record identifier. Neither a colour count nor the row number becomes a substitute identifier merely because it happens to be unique in this small version. A point table should keep the ID-to-pair mapping alongside its numerical coordinates. An unlabeled point at (5, 7) may show where a value pair sits, but the retained ID E is what lets a reviewer trace that pair back to the source card. 2. Sort whole records, not one coordinate at a time Suppose a reader wants to see the cards in ascending order of orange-dot count. Move the entire record when sorting: its ID, blue count and orange count travel together. The legitimate order is D, B, C, E, A. The corresponding pairs are D:(4, 1), B:(2, 3), C:(3, 5), E:(5, 7), A:(1, 8). The order of the rows has changed, but each card still supplies exactly the same pair. A scatterplot of these records should therefore contain the same five ID-to-coordinate assignments as the source version. This is a different operation from independently sorting the x column and the y column. Independent sorting forgets which y originally belongs with which x. A plotting program can still draw the resulting numbers; its ability to render them does not verify that they came from intact records. Row order may matter for a separate task, such as showing a sequence. That task needs an explicit sequence field and an appropriate display rule. In this exercise, sorting a point table does not create a time order or justify drawing connecting lines between the points. 3. Diagnose a tidy table that contains false pairs Here is an intentionally incorrect teaching example. Someone kept the x column and IDs in their original order but sorted only the y values from smallest to largest: Display row; Claimed Card ID; Blue dots, x; Independently sorted orange dots, y 1; A; 1; 1 2; B; 2; 3 3; C; 3; 5 4; D; 4; 7 5; E; 5; 8 This is not a corrected dataset. It is the error to inspect. Card A has been assigned D's orange count, D has been assigned E's, and E has been assigned A's. Cards B and C happen to retain their original pairs. Those two coincidences do not validate the other three rows. The repair is to recover each card's own y value from the source records. Do not simply choose whichever rearrangement produces an appealing pattern. If the identifier mapping has been lost and the source cannot be recovered, the original pairs are unresolved; a plausible reconstruction is not a verified repair. 4. Use checks that can see the pairing error Both the source table and the incorrect table have the same separate column totals: x sums to 15 and y sums to 24. Their separate column means are also the same: 3 blue dots and 24/5, or 4.8, orange dots. The x range remains 1 to 5 and the y range remains 1 to 8. These checks describe the individual columns and can all pass while the ID-to-pair mapping is wrong. A check involving both coordinates can reveal this particular alteration. In the source version, the sum of x multiplied by y within each card is 8 + 6 + 15 + 4 + 35 = 68. In the incorrect table it is 1 + 6 + 15 + 28 + 40 = 90. This is an arithmetic demonstration, not a correlation estimate, statistical significance test, or claim about a real-world relationship. Even agreement on such a sum would not prove record integrity in every dataset. Compare every ID and pair with the source. Two extensions show why matching on a single value is unsafe: - In a second version, add fictional card F with x = 2 and y = 7. It shares its x value with B and its y value with E, but it is neither of those records. B:(2, 3), F:(2, 7) and E:(5, 7) must all remain separately traceable. This version has six complete records. - In a third version, also list card G with x = 4 but no recorded y count. Do not invent an orange count of zero. G cannot supply a complete coordinate pair yet. Keep it in the source inventory as an incomplete record and describe the plot as the six complete pairs, rather than pretending all seven cards were plotted. These are separate, explicitly invented versions. Do not silently mix F or G into the five-card source table when answering the base-version tasks. 5. Seven learner tasks 1. From the five-card source version, write all five ID-to-coordinate pairs. State the meanings and units of both axes. 2. Sort the source records by orange-dot count. Give the resulting ID order and explain whether any source pair changes. 3. Compare the intentionally incorrect table with the source. Which IDs have wrong pairs, and which happen to be unchanged? 4. Check the two column sums, means and ranges. Then calculate the sum of the within-row products x times y for each table. Explain why separate column checks are insufficient. 5. Add F:(2, 7) as the second version. Can F be merged with B because their x values agree, or with E because their y values agree? Give the three distinct pairs. 6. Add G with x = 4 and unrecorded y as the third version. May it be plotted at (4, 0)? State the number of source records and complete plotted pairs. 7. Write a caption for a plot of only the original five complete cards. Identify the data as fictional, name both fields, and state that each pair comes from the same source record. Trace the point (5, 7) to its card. 6. Worked answers 1. A:(1, 8), B:(2, 3), C:(3, 5), D:(4, 1), E:(5, 7). The x axis is blue-dot count per fictional card; the y axis is orange-dot count per fictional card. Both coordinates are counts of dots, but they describe different fields on the same card. Retain the card ID with the pair. 2. D, B, C, E, A. Their intact pairs are (4, 1), (2, 3), (3, 5), (5, 7), (1, 8). Sorting whole records changes their displayed order and changes no card's coordinates. 3. A, D and E are wrong. A should be (1, 8), not (1, 1); D should be (4, 1), not (4, 7); E should be (5, 7), not (5, 8). B:(2, 3) and C:(3, 5) happen to be unchanged. A partial match is not a complete source check. 4. Both x sums are 15 and both y sums are 24. Both x means are 15/5 = 3; both y means are 24/5 = 4.8. Both x ranges are 1 to 5 and both y ranges are 1 to 8. The source sum of within-card products is 68; the incorrect-table sum is 90. Sorting one column preserves that column's individual values but changes their associations with the other field and with the card IDs. A joint checksum can flag this example, but full ID-to-pair comparison is still required. 5. Keep B:(2, 3), F:(2, 7) and E:(5, 7). A match on one coordinate is not a match on record identity or on the whole pair. The second version has six complete observations, not five after a value-based merge. 6. No. An unrecorded count is not a recorded zero. This third version contains seven source records, A through G, and six complete coordinate pairs, A through F. Record G's missing y separately; exclude it from the plotted-pair set until its value is actually supplied. The plot's caption must describe that scope. 7. One suitable caption is: "Blue-dot count versus orange-dot count for five fictional cards, A through E. Each plotted coordinate pair uses the two counts from the same source card; card IDs are retained for checking. These invented counts are for a teaching exercise, not research or classroom measurements." The point (5, 7) comes from card E in this five-card source ve