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Measures of spread

The Interquartile Range (IQR)

Quartiles divide a data set into four parts with one quarter of the data points lying below the first quartile, half lying below the second quartile, and three quarters lying below the third quartile.

  • The second quartile is the median.
  • The difference between the third quartile and the first quartile is called the interquartile range (IQR).
  • Use with the median when describing skewed distributions.
  • For example consider the data points: \(50\), \(55\), \(55\), \(55\), \(62\), \(65\), \(78\), \(99\).
  • To find the first quartile, take the bottom half of the data: \(50\), \(55\), \(55\), \(55\), and find the middle value. The middle value is between \(55\) and \(55\), therefore, the first quartile is \(55\).
  • To find the third quartile, take the top half of the data: \(62\), \(65\), \(78\), \(99\), and find the middle value. The middle value is between \(65\) and \(78\), so the third quartile is \(71.5\).
  • Therefore the interquartile range, IQR is \(71.5 - 55 = 16.5 \).