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Paper Airplane Contest: Interactive Mean vs Median

Paper Airplane Contest: Interactive Mean vs Median
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2023-07-13 16:00
SequenceProbability & StatisticsSlider AnimationGraphing
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This GeoGebra example uses a paper-airplane distance data table (with adjustable flight distances) to demonstrate how changing values affects the arithmetic mean and the median. It focuses on key statistics concepts: arithmetic mean (mean), median (Median), interpretation of median via ordering, and reasoning about how edits to one or several data points can change one statistic more than the other. From the construction summary, the lesson is built with Textfield for question/input/feedback UI, and geometric/data elements using Point, Sequence, and Polygon; Shuffle is used to randomize or revisit initial conditions, while Element together with Append and Remove supports dynamic updating of data/objects. The statistics are computed directly with mean and Median, and interactive assessment is implemented using validate, showanswer, showsolution, btnValidate, attemptCount/correctCount, btnTryAgain, btnNew, and hint/solution display controls (e.g., showhint, showButtonNew/tryAgain). Suitable for grade 5–6 to introduce probability & statistics, arithmetic mean/median interpretation, and conditional tasks such as “make the mean larger” or “make the median smaller by at least 1 m.”

GeoGebra Commands & Parameters

  1. Textfield(input1) → InputBox1
  2. Textfield(input2) → InputBox2
  3. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  4. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {0, 3, 4, 5, 2, 2, 8, 7, 7, 0, 3, 4, 0, 7, 0, 9, 9, 9, 1, 5, 9, 1, 0, 10, 7, 7, 7, 5, 2, 2, 10, 7, 10, 1, 6, 4, 8, 10, 10, 10, 5, 10, 5, 4, 10, 8, 6, 6, 0, 4, 0, 9, 7, 1, 1, 7, 6, 2, 1, 8, 7, 8, 2, 4, 6, 6, 10, 0, 2, 9, 1, 0, 9, 5, 10, 6, 4, 9, 3, 1, 8, 8, 8, 4, 9, 4, 5, 4, 0, 10, 7, 1, 6, 8, 6, 2, 10, 8, 1, 7}
  5. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  6. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {9, 10, 8, 9, 1, 9, 0, 3, 6, 5, 6, 3, 0, 2, 2, 5, 6, 0, 3, 4, 5, 8, 5, 9, 10, 7, 3, 6, 3, 8, 5, 2, 1, 9, 8, 4, 7, 8, 3, 1, 6, 7, 4, 5, 2, 3, 4, 8, 6, 9, 1, 6, 9, 10, 10, 2, 10, 6, 3, 6, 2, 4, 7, 10, 0, 7, 0, 4, 7, 0, 3, 1, 6, 8, 0, 1, 4, 9, 5, 1, 2, 9, 9, 9, 5, 7, 6, 2, 1, 6, 0, 4, 1, 4, 10, 1, 6, 3, 9, 1}
  7. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  8. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  9. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  10. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  11. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  12. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  13. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  14. Defined((input1 * input2)) → fixed
  15. Point(xAxis) → O
  16. Textfield(input3) → InputBox3
  17. Textfield(input4) → InputBox4
  18. Textfield(input5) → InputBox5
  19. Textfield(input6) → InputBox6
  20. Textfield(input7) → InputBox7
  21. Textfield(input8) → InputBox8
  22. Point(xAxis) → W
  23. Point(xAxis) → Z
  24. Segment(W, Z) → p
  25. Segment(W, A_1) → q
  26. Polygon(P1, P2, C_1, B_1) → q3, p1, p2, r, b_1
  27. Polygon(P3, P4, E_1, D_1) → q4, p3, p4, e_1, s
  28. Polygon(P5, P6_{1}, G_1, F_1) → q5, p5, p6_{1}, g_1, t
  29. Polygon(P6, P7, I_1, H_1) → q6, p6, p7, i_1, h_1
  30. Polygon(P8, P9, K_1, J_1) → q7, p8, p9, k_1, j_1
  31. Polygon(P10, P11, M_1, L_1) → q8, p10, p11, m_1, l_1
  32. Polygon(P12, P13, O_1, N_1) → q9, p12, p13, o_1, n_1
  33. Polygon(P14, P15, Q_1, P_1) → q10, p14, p15, q_1, p_1
  34. mean({input1, input2, input3, input4, input5, input6, input7, input8}) → mittelw
  35. Median({input1, input2, input3, input4, input5, input6, input7, input8}) → med
  36. Segment(R_1, S_1) → r_1
  37. Segment(T_1, U_1) → s_1
  38. Segment(H, I) → f
  39. Segment(E, PKT3) → g
  40. Segment(F, PKT4) → h
  41. Segment(H, F) → i
  42. Segment(G, PKT2) → j
  43. Segment(I, PKT4) → k
  44. Polygon(G, PKT2, F, H) → q1, g_2, pkt2, f_1, h_2
  45. Segment(J, T) → l
  46. Segment(K, U) → m
  47. Segment(L, V) → n
  48. Segment(M, V_1) → b
  49. Segment(P, W_1) → c
  50. Segment(Q, Z_1) → d
  51. Segment(S, A_2) → e
  52. Sequence((-5, (i * 0.7)), i, 0, 9) → l2
  53. Sequence(Segment[(-5.1, (i * 0.7)), (-4.9, (i * 0.7))], i, 1, 9) → l4
  54. Sequence(Text["\textsf{" + (i - 1) + "}", l2(i) + (-0.3, 0.05), false, true, 0, 0], i, 1, Length[l2]) → l3

AI Drawing Prompt Reference

Create an interactive chart for a paper airplane contest showing how the mean and median change with flight distances. Start by drawing a rectangle, then generate 100 unique X and Y coordinates between 0 and 10, removing duplicates. Next, plot these points and calculate the mean and median of the input values. Finally, draw several polygons and segments to illustrate the changes in mean and median.
The prompt above was compiled from the original drawing commands and is for reference only.