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PSAT Math · Question of the Day

PSAT Math Question of the Day

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Wednesday, August 12, 2026

A box plot (five-number summary) represents the distribution of times (in minutes) to complete a puzzle for a group of students: minimum 5, Q1=8Q_1=8, median 10, Q3=14Q_3=14, maximum 30. What is the interquartile range (IQR), and what is the range?

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A box plot (five-number summary) represents the distribution of times (in minutes) to complete a puzzle for a group of students: minimum 5, Q1=8Q_1=8, median 10, Q3=14Q_3=14, maximum 30. What is the interquartile range (IQR), and what is the range?

  1. IQR 6; range 22
  2. IQR 6; range 25 (correct answer)
  3. IQR 9; range 22
  4. IQR 9; range 25

Explanation: The question asks for the interquartile range (IQR) and range from a box plot with minimum 5, Q1=8, median 10, Q3=14, maximum 30. The IQR is Q3 minus Q1, so 14 - 8 = 6, representing the spread of the middle 50% of times. The range is maximum minus minimum, or 30 - 5 = 25, showing the full spread including outliers. These measures highlight different aspects: IQR resists extremes, while range includes them. A key error is subtracting median instead of Q1 from Q3 for IQR. When reading box plots, note that IQR focuses on central spread, making it useful for comparing distributions; verify by direct subtraction.