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Arithmetic mean – sharing equally and balancing

MathematicsStatisticsAges 15–16

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Four screens explore the arithmetic mean. Level Out: pour water between connected cups and watch the water level move to exactly the mean; Share Candy: move whole candies between plates and discover that the mean is not always a whole number; Share Apples: cut the leftover apples into fractions to share perfectly fairly; Balance Point: place a fulcrum on a number line so that the sum of signed deviations is 0. Students drag water levels, candies, apple pieces and the fulcrum, and the numbers update according to x̄ = (Σxᵢ)/n. Based on the "Mean: Share and Balance" simulation by PhET Interactive Simulations, University of Colorado Boulder (CC BY 4.0); rewritten.

Lesson: Mean of a data set

How to use

Parameters you can change

  • Screen Level Out, Share Candy, Share Apples, Balance Point
  • Number of cups (Level Out) 3–5
  • Number of plates (Share Candy, Share Apples) 2–5
  • Number of apples (Share Apples) 1–12 apples
  • Data (Balance Point, comma-separated)
  • Show mean line/point

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