A rank can change while its source value stays the same
Five invented records compare two explicit ranking rules. Adding Fern with 8 tokens changes Dune and Elm's competition ranks from 4 to 5, while their counts stay at 5. The table shows the original population.
Original five-record fictional table: Aster has 12 toy tokens, competition rank 1 and dense rank 1; Birch and Cedar each have 8, rank 2 under both rules; Dune and Elm each have 5, competition rank 4 and dense rank 3. Fern and Gale are not included.
Purpose and invented source
This table-and-paper activity asks why a reported rank can change when the value assigned to a record has not changed. All names and counts are invented for this exercise. They do not describe people, actual inventories, experiments, product performance or learning outcomes. No software or account is needed to work through the questions. The table contains the original five-record population only; the later addition of Fern is a separate scenario, not a silent change to that table.
Define two ranking rules
Source Card R assigns toy-token counts to five distinct records: Aster 12, Birch 8, Cedar 8, Dune 5 and Elm 5. Higher counts come first. These counts are arbitrary practice values, not quality ratings. For this activity, competition rank means 1 plus the number of records with a strictly greater count. Dense rank means 1 plus the number of distinct count values that are strictly greater. Equal counts receive equal ranks under both rules. The ranks have no token unit. State which definition is used; do not assume a numbered position supplies one.
Read the authored table
Aster has competition rank 1 and dense rank 1. Birch and Cedar both have competition rank 2 and dense rank 2. Dune and Elm both have competition rank 4 and dense rank 3. Three records have more than 5 tokens, but only two distinct values, 12 and 8, are greater than 5. That explains the two different rank labels for Dune and Elm. The rank columns were entered by the author from these definitions. This visualization is not evidence that a product automatically computes or verifies ranking rules. If a viewer sorts the table, identify records by name; a new display order does not recalculate these authored columns.
Try six questions
1. Why is Dune fourth under competition rank but third under dense rank? 2. On the dense-rank scale, Aster to Birch and Birch to Dune each differ by one rank. Are their toy-token differences equal? 3. Does Cedar being displayed after Birch establish that Cedar has fewer tokens? 4. Add a sixth record, Fern, with 8 tokens, keeping every original value unchanged. Give the competition and dense ranks of all six records. Which original ranks change? 5. A revision uses the six-record population but retains Dune's old competition rank 4. What must be repaired? 6. In a separate scenario, add Gale, whose count is unknown, to the original five records. Can it be put below Elm by entering zero? What can the table report instead?
Worked answers: rules and margins
1. Dune has three records above it: Aster, Birch and Cedar. Its competition rank is therefore 1 + 3 = 4. There are only two distinct greater counts, 12 and 8, so its dense rank is 1 + 2 = 3. Neither definition changes Dune's assigned count of 5. 2. The token differences are 12 - 8 = 4 and 8 - 5 = 3. Equal one-rank gaps do not establish equal gaps in the source unit. A rank is not a token amount. 3. No. Both records have count 8 and rank 2 under both definitions. An alphabetical display tie-break puts Birch before Cedar for readability; it supplies no additional quantity or merit. Do not turn that display position into a unique numerical advantage.
Worked answers: change the population
4. With Fern included, competition ranks are Aster 1, Birch 2, Cedar 2, Fern 2, Dune 5 and Elm 5. Four records now have counts strictly greater than 5. Dense ranks are Aster 1, Birch 2, Cedar 2, Fern 2, Dune 3 and Elm 3, because the distinct greater values are still 12 and 8. Dune and Elm change from competition rank 4 to 5 even though their counts remain 5. This is a change in the comparison population, not evidence that their own counts fell. 5. Retaining rank 4 would mix populations under the stated competition rule. Recompute the affected ranks and identify the six-record version in the caption. Keep the original five-record version for comparison rather than overwriting its values or pretending that the two tables use the same population. 6. An unknown count is not zero. Keep Gale as count unknown and rank not calculated under these rules until a valid count is supplied. Do not invent a zero to force a last-place rank. A supplied zero would be a real value within this fictional exercise and would answer a different source question. Ranks for the complete population are not final either: Gale could have a count greater than the known values. You may display explicitly labelled ranks among the five known-count records only, with Gale unranked and excluded from that comparison. Otherwise, withhold complete-population ranks until its count is resolved.
Write a reviewable caption
For the original table, one caption is: "Five invented records ranked by assigned toy-token count, higher first. Competition rank is one plus the number of records with a strictly greater count; dense rank is one plus the number of distinct greater counts. Equal counts share ranks. Alphabetical order resolves display ties only. The original population excludes Fern and Gale." For the Fern scenario, name the six-record population and update the rank results together. Keep a six-field review note: source version and population; record name; unchanged assigned count and unit; exact ranking definition; resulting rank; reason for any change. For Dune after Fern is added, record Card R plus Fern; Dune; 5 toy tokens; competition rule above; rank 5; one additional record now lies above it. Do not describe a lower rank number as a smaller measurement or a higher number as measured deterioration.
Credit, limits and reuse
Created by Figran Team, associated with Figran, a commercial AI-assisted scientific visual creation service. This original teaching activity was prepared with AI assistance and checked against its declared rank formulas and arithmetic. It is a proposed exercise, not an independent product review, classroom trial or scientific finding. The original teaching text and fictional source-card data are offered under Creative Commons Attribution 4.0 International: https://creativecommons.org/licenses/by/4.0/ . Attribute Figran Team and this title, link the licence and indicate changes. This licence does not cover Figran software, brand assets or the Datawrapper platform. Public contact: [email protected]. The linked creator website is Figran's commercial product website, not a measured dataset or evidence of benefits.
This table-and-paper activity asks why a reported rank can change when the value assigned to a record has not changed. All names and counts are invented for this exercise. They do not describe people, actual inventories, experiments, product performance or learning outcomes. No software or account is needed to work through the questions. The table contains the original five-record population only; the later addition of Fern is a separate scenario, not a silent change to that table.
Define two ranking rules
Source Card R assigns toy-token counts to five distinct records: Aster 12, Birch 8, Cedar 8, Dune 5 and Elm 5. Higher counts come first. These counts are arbitrary practice values, not quality ratings. For this activity, competition rank means 1 plus the number of records with a strictly greater count. Dense rank means 1 plus the number of distinct count values that are strictly greater. Equal counts receive equal ranks under both rules. The ranks have no token unit. State which definition is used; do not assume a numbered position supplies one.
Read the authored table
Aster has competition rank 1 and dense rank 1. Birch and Cedar both have competition rank 2 and dense rank 2. Dune and Elm both have competition rank 4 and dense rank 3. Three records have more than 5 tokens, but only two distinct values, 12 and 8, are greater than 5. That explains the two different rank labels for Dune and Elm. The rank columns were entered by the author from these definitions. This visualization is not evidence that a product automatically computes or verifies ranking rules. If a viewer sorts the table, identify records by name; a new display order does not recalculate these authored columns.
Try six questions
1. Why is Dune fourth under competition rank but third under dense rank? 2. On the dense-rank scale, Aster to Birch and Birch to Dune each differ by one rank. Are their toy-token differences equal? 3. Does Cedar being displayed after Birch establish that Cedar has fewer tokens? 4. Add a sixth record, Fern, with 8 tokens, keeping every original value unchanged. Give the competition and dense ranks of all six records. Which original ranks change? 5. A revision uses the six-record population but retains Dune's old competition rank 4. What must be repaired? 6. In a separate scenario, add Gale, whose count is unknown, to the original five records. Can it be put below Elm by entering zero? What can the table report instead?
Worked answers: rules and margins
1. Dune has three records above it: Aster, Birch and Cedar. Its competition rank is therefore 1 + 3 = 4. There are only two distinct greater counts, 12 and 8, so its dense rank is 1 + 2 = 3. Neither definition changes Dune's assigned count of 5. 2. The token differences are 12 - 8 = 4 and 8 - 5 = 3. Equal one-rank gaps do not establish equal gaps in the source unit. A rank is not a token amount. 3. No. Both records have count 8 and rank 2 under both definitions. An alphabetical display tie-break puts Birch before Cedar for readability; it supplies no additional quantity or merit. Do not turn that display position into a unique numerical advantage.
Worked answers: change the population
4. With Fern included, competition ranks are Aster 1, Birch 2, Cedar 2, Fern 2, Dune 5 and Elm 5. Four records now have counts strictly greater than 5. Dense ranks are Aster 1, Birch 2, Cedar 2, Fern 2, Dune 3 and Elm 3, because the distinct greater values are still 12 and 8. Dune and Elm change from competition rank 4 to 5 even though their counts remain 5. This is a change in the comparison population, not evidence that their own counts fell. 5. Retaining rank 4 would mix populations under the stated competition rule. Recompute the affected ranks and identify the six-record version in the caption. Keep the original five-record version for comparison rather than overwriting its values or pretending that the two tables use the same population. 6. An unknown count is not zero. Keep Gale as count unknown and rank not calculated under these rules until a valid count is supplied. Do not invent a zero to force a last-place rank. A supplied zero would be a real value within this fictional exercise and would answer a different source question. Ranks for the complete population are not final either: Gale could have a count greater than the known values. You may display explicitly labelled ranks among the five known-count records only, with Gale unranked and excluded from that comparison. Otherwise, withhold complete-population ranks until its count is resolved.
Write a reviewable caption
For the original table, one caption is: "Five invented records ranked by assigned toy-token count, higher first. Competition rank is one plus the number of records with a strictly greater count; dense rank is one plus the number of distinct greater counts. Equal counts share ranks. Alphabetical order resolves display ties only. The original population excludes Fern and Gale." For the Fern scenario, name the six-record population and update the rank results together. Keep a six-field review note: source version and population; record name; unchanged assigned count and unit; exact ranking definition; resulting rank; reason for any change. For Dune after Fern is added, record Card R plus Fern; Dune; 5 toy tokens; competition rule above; rank 5; one additional record now lies above it. Do not describe a lower rank number as a smaller measurement or a higher number as measured deterioration.
Credit, limits and reuse
Created by Figran Team, associated with Figran, a commercial AI-assisted scientific visual creation service. This original teaching activity was prepared with AI assistance and checked against its declared rank formulas and arithmetic. It is a proposed exercise, not an independent product review, classroom trial or scientific finding. The original teaching text and fictional source-card data are offered under Creative Commons Attribution 4.0 International: https://creativecommons.org/licenses/by/4.0/ . Attribute Figran Team and this title, link the licence and indicate changes. This licence does not cover Figran software, brand assets or the Datawrapper platform. Public contact: [email protected]. The linked creator website is Figran's commercial product website, not a measured dataset or evidence of benefits.