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Book Moving Mode: Exploring the Mode of a Data Set

Book Moving Mode: Exploring the Mode of a Data Set
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2024-01-25 04:38
This example demonstrates how the mode changes as numbers in a data set are adjusted. The core mathematical concept is the mode in statistics, which is the value that appears most frequently. Construction involves using GeoGebra commands like RandomUniform, Take, and Mode to dynamically generate data sets and observe mode changes. Suitable for Grades 6-8 students to learn data description and statistical characteristics.

GeoGebra Commands & Parameters

  1. RandomUniform(0, 0.999, 200) → allRandomSeeds, {0.00682835687692941, 0.31751022864865613, 0.9469613743473014, 0.3802444348220913, 0.6776929754420038, 0.76428214240365, 0.8074903808372758, 0.42606040125808403, 0.16512834660239661, 0.24826002432011507, 0.11240457172647836, 0.8415839349211803, 0.6478526976109029, 0.13202811117378058, 0.36583838804715574, 0.6636353416699518, 0.6846096037975458, 0.41175457107435387, 0.686151331089769, 0.8377468165485289, 0.9906177082689095, 0.5517031057013612, 0.6902078178397075, 0.7092477992047876, 0.5108814465125537, 0.5691814575847132, 0.46302645707550466, 0.2427175927249931, 0.8650746774832339, 0.6941446446753122, 0.18008336216497606, 0.6400144673341323, 0.73715975053333, 0.9256461012360586, 0.5534914018637197, 0.7889260276858454, 0.7370766232393213, 0.5907744746686963, 0.9114315900435689, 0.009288450883655317, 0.8247260057302246, 0.5726268828503165, 0.3765875382103911, 0.909195696003367, 0.41407831855723787, 0.2292510800888336, 0.31292652513316344, 0.779660133842514, 0.8725681211724167, 0.1323398371422842, 0.9429819308949486, 0.8067964186799411, 0.2589796019492774, 0.6827800038205126, 0.7808225653431936, 0.6152790654083498, 0.7617923313369603, 0.33494671251879754, 0.3231429920242129, 0.05647177538660486, 0.5294413547806932, 0.6278904144365258, 0.27337709458600923, 0.919242402865092, 0.23714664616000064, 0.49728957744672175, 0.41042326049488304, 0.2590628064260239, 0.032888585319304026, 0.33623638934385414, 0.10247528933696123, 0.3055464361054644, 0.2417452642473024, 0.12258604751239872, 0.3825766985008646, 0.5470987537677369, 0.5321662092233089, 0.5007317591118822, 0.45585926912719354, 0.38884711199499755, 0.07683405705075973, 0.0972683773861889, 0.46698785703450824, 0.9614763938793055, 0.6095616461984681, 0.4890769153627955, 0.38711402665342826, 0.07602568890354981, 0.19318672940627651, 0.21090009732884746, 0.9036401171897975, 0.9970985214191458, 0.9086595918369569, 0.867486241392294, 0.2793125620243331, 0.747305506589311, 0.6904716972515148, 0.9638539371430846, 0.23060075370244987, 0.8450931290715474, 0.9652434341961598, 0.30217481352406206, 0.04297230700064626, 0.009416172953283277, 0.835679473997153, 0.8941843673799411, 0.26354957350403724, 0.12198398400912645, 0.05620839873389889, 0.17291283140161837, 0.5447256284620218, 0.9040511007473002, 0.1664501969979999, 0.8848786570090562, 0.4156289278269999, 0.1149341834788675, 0.7592013303030373, 0.5127065368679373, 0.02885616201691667, 0.7676144501302903, 0.995891718263658, 0.18941976991933113, 0.2176423046685914, 0.8369332039187518, 0.17945150361085982, 0.10841404242081612, 0.5206038915216938, 0.11200386418677707, 0.39722718375772914, 0.1323447836082933, 0.17737883123343767, 0.41954904843051705, 0.004008003512221686, 0.859854866110026, 0.48889089661725393, 0.21792468858894934, 0.9553630390012293, 0.7222325766850765, 0.357591004809697, 0.624616193093794, 0.8593477911460576, 0.7607214673310142, 0.24587046819859812, 0.33998198064186425, 0.8912162141372134, 0.6393041187182122, 0.2979029593691161, 0.5279807508689179, 0.6440699154098132, 0.07435179623196501, 0.8564515362550251, 0.67754651246909, 0.3383912996390664, 0.320569176041315, 0.15967695105933719, 0.6381737247656496, 0.7741402611771987, 0.5721710395420363, 0.5577010430081958, 0.5321405897748966, 0.861546770987795, 0.12320283403602844, 0.22561472232644186, 0.002633523401810604, 0.5519019588129788, 0.9293614043455896, 0.929776689589217, 0.3028400025872535, 0.5305406939011422, 0.7815856569484456, 0.13162186698075773, 0.07284879670732249, 0.07981618133104883, 0.6130683831197784, 0.3447919820846296, 0.2369381601547729, 0.10119531826697108, 0.6361909080877599, 0.4572119675908611, 0.3785427723407819, 0.42164814858117955, 0.8722023638897075, 0.4217662954745206, 0.09186827237092605, 0.1392707765129701, 0.34625236118128855, 0.5594781288290942, 0.28177015801719035, 0.9525633104339716, 0.6786437385364532, 0.5165622757785356, 0.11813012858838383, 0.14298743598459537, 0.07389660953807693, 0.7714092066157594, 0.3525474851456436, 0.08334843158871108, 0.704410529417889, 0.48046266626696266, 0.026717120346035527}
  2. RandomUniform(0, 0.999, 200) → randomBookSeeds, {0.9791868307812335, 0.35117308374063516, 0.3520778579955978, 0.15438841300652686, 0.7987223638954207, 0.6970968883021179, 0.2027890790171682, 0.8462898430207696, 0.2099711468809086, 0.10916567707388462, 0.8079782698284665, 0.46686477210633165, 0.7214516530742029, 0.8406411528326035, 0.6867152517034947, 0.8390922876399405, 0.10641099992526927, 0.5831193010578165, 0.4785402967419313, 0.2400643672499305, 0.6097353861235413, 0.9552319410580133, 0.6681766335760645, 0.8703568462196534, 0.44366123387188733, 0.08126533728110975, 0.49459775478073686, 0.8035670409520352, 0.5100745081750899, 0.6309111106653338, 0.02052911591240922, 0.9096938962415028, 0.3695748445989745, 0.8187790920514411, 0.5103380998905852, 0.13230962324178647, 0.9895902904824233, 0.6421818773710241, 0.45835899652066436, 0.5617125523462647, 0.921654674795121, 0.3170533168204229, 0.8210108282990327, 0.18146123126654656, 0.14850664983904516, 0.2466808967793749, 0.29759670329617305, 0.788868209437712, 0.016932753482127104, 0.05822104231837302, 0.7554219544641435, 0.6021797159408366, 0.34026155934788455, 0.20572290933117082, 0.2588363143083312, 0.24328324942427876, 0.9601172018993481, 0.3986115586198231, 0.4649918515518046, 0.3518705925132804, 0.8144618861242026, 0.635276373052192, 0.5875135854977681, 0.8530369153913744, 0.8200965121094493, 0.944572930494437, 0.493903936645548, 0.9903194383757424, 0.6996469926148282, 0.028678869802904336, 0.9833446202213842, 0.5951704351500055, 0.1996409488620012, 0.8688448281623379, 0.7576214186616145, 0.7078187600466755, 0.02957548921756143, 0.044150612978183436, 0.09617745258066941, 0.588403554260233, 0.24889108203932547, 0.8884151446829445, 0.8067994199811148, 0.34916061782119523, 0.7525004525542658, 0.9199151921855309, 0.5861592518918345, 0.9413084786006949, 0.9749731481191084, 0.8825440982218864, 0.5063700991441747, 0.9891160323492848, 0.9216475045246224, 0.6014853097296203, 0.021870921543470145, 0.0014374237983715147, 0.1648312554213227, 0.36638917877814764, 0.509327601814468, 0.8367721266938003, 0.48986086552955704, 0.9254229793724791, 0.08783198567851269, 0.9116497046016518, 0.48011600504076596, 0.2944149576705981, 0.15649077252735205, 0.4948482737529667, 0.4181322607947625, 0.47763220270669415, 0.8885277974557845, 0.6586347327028712, 0.5647196241071855, 0.9215207844252137, 0.6732705511907052, 0.8748623142459876, 0.03447720517605579, 0.946992752537259, 0.33286149341069793, 0.9843766997876469, 0.20129750332888777, 0.6895706349854339, 0.8052194881619652, 0.296767839750647, 0.8263739845216643, 0.0988942620671192, 0.8506830626112373, 0.8610572175564903, 0.8518655134781934, 0.35775800935374713, 0.25589093453652123, 0.548433762297257, 0.12472962823615125, 0.6869780807106225, 0.9677977541643014, 0.4096420562093968, 0.15031358078190396, 0.8609900607125228, 0.5662849320988079, 0.9610871129059205, 0.3450883474268025, 0.9351468173135431, 0.4646063927330308, 0.4381479330842967, 0.14342497774957302, 0.6132241444142518, 0.31790833724186296, 0.7655903873321499, 0.7605466365164958, 0.40364903904701505, 0.1412797139732497, 0.007335470610682147, 0.37574113207791787, 0.22044063394836194, 0.7722265680200676, 0.27417423998834406, 0.9685903415118846, 0.3577984289742533, 0.43911919278895933, 0.6753245506651026, 0.1103620577164726, 0.8396854378980623, 0.34703409926868267, 0.6729968964080743, 0.5088184212731488, 0.9846356371997895, 0.42050672193830185, 0.34837804307037223, 0.26152217351717133, 0.6523658938023913, 0.536021295919407, 0.46265119686762873, 0.3172680574218311, 0.05059161502413006, 0.8575953533803808, 0.8738499194744135, 0.8595309808869105, 0.16373365901517378, 0.17356477643374205, 0.8194905149985581, 0.9638062486051661, 0.8399608828643318, 0.4446436013138285, 0.8140441397227293, 0.10841920693946887, 0.3172380437390315, 0.15151871040514162, 0.4323943672449833, 0.8608025819690664, 0.5007434543752366, 0.3726455416268955, 0.03448000190583896, 0.34737943053490705, 0.6391835924044014, 0.9845342794673758, 0.5793452026226951, 0.8780479230722857, 0.10416387497498729, 0.7866591546080429, 0.03281042507009921}
  3. Take(allRandomSeeds, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
  4. Corner(5) → layoutAppSize
  5. onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], onboardingCase, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset
  6. PixelsToPoint(Corner[1], Corner[3], Corner[5], (11, 400)) → AnchorLeft
  7. PixelsToPoint(Corner[1], Corner[3], Corner[5], (11 + shelfWidthPX, 400)) → AnchorRight
  8. PixelsToPoint(Corner[1], Corner[3], Corner[5], (11, 277)) → AnchorShelfB
  9. PixelsToPoint(Corner[1], Corner[3], Corner[5], (11, 162)) → AnchorShelfA
  10. Flatten(Zip[Sequence[(x(AnchorLeft) + pointGap + (B * (pointGap + pointBookWidth)), y(A) + pointGap / 2), B, 0, 3], A, {AnchorShelfA, AnchorShelfB, AnchorLeft + (0, (1.5 * pointGap / 2))}]) → allShelfPositions
  11. Translate(clickTemplate, allShelfPositions(1)) → clickA1
  12. Translate(clickTemplate, allShelfPositions(2)) → clickA2
  13. Translate(clickTemplate, allShelfPositions(3)) → clickA3
  14. Translate(clickTemplate, allShelfPositions(4)) → clickA4
  15. Translate(clickTemplate, allShelfPositions(6)) → clickB2
  16. Translate(clickTemplate, allShelfPositions(5)) → clickB1
  17. Translate(clickTemplate, allShelfPositions(7)) → clickB3
  18. Translate(clickTemplate, allShelfPositions(8)) → clickB4
  19. Translate(clickTemplate, allShelfPositions(9)) → clickC1
  20. Translate(clickTemplate, allShelfPositions(10)) → clickC2
  21. Translate(clickTemplate, allShelfPositions(11)) → clickC3
  22. Translate(clickTemplate, allShelfPositions(12)) → clickC4
  23. Element(Remove[Sequence[1, 12], {currentIndices(pick)}], 1 + floor((randomBookSeeds(bookIndex) * 11))) → nextBookIndex
  24. If(countQuestion ≟ 0, startingBooks, Sequence[1 + floor((currentRandomSeeds(A) * 12)), A, 1, 12]) → randomIndices
  25. Mode(randomIndices) → modeRandom
  26. Sequence(If[i ≟ pick, If[currentIndices(i) ≟ cEMPTY, nextBookIndex, cEMPTY], currentIndices(i)], i, 1, 12) → possibleNewBooks
  27. Mode(Remove[Take[currentIndices, 1, 12], Sequence[cEMPTY, A, 1, CountIf[x ≟ cEMPTY, currentIndices]]]) → modeCurrent
  28. PixelsToPoint((xMin, yMin), (xMax, yMax), (800, 500), (400, 200)) → AnchorMode
  29. Zip(A + AnchorMode - allShelfPositions(1), A, allShelfPositions) → allModePositions
  30. Zip(If[B ≟ 1, Translate[bookA, A]], A, Join[{allShelfPositions, allModePositions}], B, currentIndices) → displayBookA
  31. Zip(If[B ≟ 2, Translate[bookB, A]], A, Join[{allShelfPositions, allModePositions}], B, currentIndices) → displayBookB
  32. Zip(If[B ≟ 3, Translate[bookC, A]], A, Join[{allShelfPositions, allModePositions}], B, currentIndices) → displayBookC
  33. Zip(If[B ≟ 4, Translate[bookD, A]], A, Join[{allShelfPositions, allModePositions}], B, currentIndices) → displayBookD
  34. Zip(If[B ≟ 5, Translate[bookE, A]], A, Join[{allShelfPositions, allModePositions}], B, currentIndices) → displayBookE
  35. Zip(If[B ≟ 6, Translate[bookF, A]], A, Join[{allShelfPositions, allModePositions}], B, currentIndices) → displayBookF
  36. Zip(If[B ≟ 7, Translate[bookG, A]], A, Join[{allShelfPositions, allModePositions}], B, currentIndices) → displayBookG
  37. Zip(If[B ≟ 8, Translate[bookH, A]], A, Join[{allShelfPositions, allModePositions}], B, currentIndices) → displayBookH
  38. Zip(If[B ≟ 9, Translate[bookI, A]], A, Join[{allShelfPositions, allModePositions}], B, currentIndices) → displayBookI
  39. Zip(If[B ≟ 10, Translate[bookJ, A]], A, Join[{allShelfPositions, allModePositions}], B, currentIndices) → displayBookJ
  40. Zip(If[B ≟ 11, Translate[bookK, A]], A, Join[{allShelfPositions, allModePositions}], B, currentIndices) → displayBookK
  41. Zip(If[B ≟ 12, Translate[bookL, A]], A, Join[{allShelfPositions, allModePositions}], B, currentIndices) → displayBookL
  42. Mode(Remove[possibleNewBooks, Sequence[cEMPTY, A, 1, CountIf[x ≟ cEMPTY, possibleNewBooks]]]) → modePossible
  43. Translate(Dilate[bookA, 1 + pulsing / 4, (pointBookWidth / 2, pointBookWidth / 2)], allShelfPositions(11)) → pulsingBook

AI Drawing Prompt Reference

Create a dynamic bookshelf with randomly generated books. Books are distributed across three shelves, and users can click on books to view details. The positions of the shelves and books will adjust dynamically based on user interactions. The mode (most frequently occurring book) will change as books are adjusted and is displayed next to the shelves.
The prompt above was compiled from the original drawing commands and is for reference only.