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Comparing Random Quotients

Comparing Random Quotients
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2015-11-07 08:12
SequenceProbability & StatisticsGeometric Construction
This example demonstrates how to compare the sizes of randomly generated quotients using GeoGebra. Core math concepts include division operations, sequences, size comparison, and median values. Key GeoGebra commands and objects used in the construction are Sequence (for generating sequences), Intersect (for calculating intersections), Point (for point creation), Segment (for drawing segments), Vector (for vector representation), If (for conditional logic), and Remove (for object removal). Suitable for high school mathematics education to understand the distribution of random variables and comparison in probability and statistics.

GeoGebra Commands & Parameters

  1. Sequence(Random[2, 9], i, 1, n) → factor1
  2. Sequence((Element[factor1, i] * Random[2, 9]), i, 1, n) → product
  3. Sequence(Element[product, i] / Element[factor1, i], i, 1, n) → answer
  4. Intersect(xAxis, yAxis) → A
  5. Point(xAxis) → B
  6. Segment(A, B) → a
  7. Sequence(Polygon[A + ((20 / (n - 1) * i), 0), A + (4, 0) + ((20 / (n - 1) * i), 0), 4], i, 0, n - 1) → rects
  8. Vector(C, D) → u
  9. If(IsInRegion[ONE, Element[rects, 1]], 1, (IsInRegion[ONE, Element[rects, 2]] * 2) + (IsInRegion[ONE, Element[rects, 3]] * 3) + (IsInRegion[ONE, Element[rects, 4]] * 4) + (IsInRegion[ONE, Element[rects, 5]] * 5)) → order1
  10. If(IsInRegion[TWO, Element[rects, 1]], 1, (IsInRegion[TWO, Element[rects, 2]] * 2) + (IsInRegion[TWO, Element[rects, 3]] * 3) + (IsInRegion[TWO, Element[rects, 4]] * 4) + (IsInRegion[TWO, Element[rects, 5]] * 5)) → order2
  11. If(IsInRegion[THREE, Element[rects, 1]], 1, (IsInRegion[THREE, Element[rects, 2]] * 2) + (IsInRegion[THREE, Element[rects, 3]] * 3) + (IsInRegion[THREE, Element[rects, 4]] * 4) + (IsInRegion[THREE, Element[rects, 5]] * 5)) → order3
  12. If(IsInRegion[FOUR, Element[rects, 1]], 1, (IsInRegion[FOUR, Element[rects, 2]] * 2) + (IsInRegion[FOUR, Element[rects, 3]] * 3) + (IsInRegion[FOUR, Element[rects, 4]] * 4) + (IsInRegion[FOUR, Element[rects, 5]] * 5)) → order4
  13. If(IsInRegion[FIVE, Element[rects, 1]], 1, (IsInRegion[FIVE, Element[rects, 2]] * 2) + (IsInRegion[FIVE, Element[rects, 3]] * 3) + (IsInRegion[FIVE, Element[rects, 4]] * 4) + (IsInRegion[FIVE, Element[rects, 5]] * 5)) → order5
  14. Remove(First[{order1, order2, order3, order4, order5}, n], {0, 0, 0, 0, 0}) → PlacedAnswers