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Summary statistics, IQR and outliers

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Useful for: IB Math AA SL & HL IB Math AI SL & HL AP® Statistics

Learn it Q1 and Q3 split the data into quarters; IQR = Q3 − Q1. A value is an outlier if it is below Q1 − 1.5·IQR or above Q3 + 1.5·IQR. Adding a constant to every value shifts the mean and median but not the spread; multiplying scales both.

Example: Q1 = 20, Q3 = 32. Is 52 an outlier?

  1. IQR = 12; upper fence = 32 + 18 = 50.
  2. 52 > 50, so yes.

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