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Pre-Algebra · Question of the Day

Pre-Algebra Question of the Day

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Monday, November 2, 2026

A box plot displays the heights (in inches) of basketball players on a team. The plot shows that Q1 = 70 inches and Q3 = 76 inches. A coach states that "the team has good height consistency since most players are within 6 inches of each other." Evaluate the accuracy of the coach's reasoning.

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A box plot displays the heights (in inches) of basketball players on a team. The plot shows that Q1 = 70 inches and Q3 = 76 inches. A coach states that "the team has good height consistency since most players are within 6 inches of each other." Evaluate the accuracy of the coach's reasoning.

  1. The coach's reasoning is correct because the IQR of 6 inches shows that 75% of players are within this range
  2. The coach's reasoning is incorrect because the IQR of 6 inches represents only 50% of players, not most of the team (correct answer)
  3. The coach's reasoning is correct because an IQR of 6 inches indicates low variability for basketball player heights
  4. The coach's reasoning is incomplete because we need the full range from minimum to maximum to assess consistency

Explanation: IQR = Q3 - Q1 = 76 - 70 = 6 inches, but this represents the range containing the middle 50% of players, not 'most' of the team. The coach incorrectly interprets what the IQR represents. Choice A incorrectly states the IQR covers 75%. Choice C makes a judgment about what constitutes 'low variability' without context. Choice D misses the main error in the coach's reasoning about what percentage the IQR represents.