4-4 The median recap, quartiles and the interquartile range

• Sort the data, then split it: Q1 is the median of the lower half, Q2 is the median of the whole set, Q3 the median of the upper half.
• Interquartile range (IQR) = Q3 − Q1 — the spread of the middle 50% of the data, and unlike the range it is not distorted by extreme values.
• When the count is odd, the common school convention excludes the middle value from both halves.
• Half of the data always lies inside the interval [Q1, Q3], which is why the IQR is used to judge consistency of the bulk of the observations.

Worked example

• Data 4, 6, 7, 9, 14 sorted: median Q2 = 7, lower half {4, 6} → Q1 = 5, upper half {9, 14} → Q3 = 11.5, so IQR = 6.5 and range = 10.