5.6.2 Quartiles when the sample size is awkward

For the six ordered data items 1, 3, 3, 6, 7, 7, the lower quartile is given by

In other words, the lower quartile q_L is given by the number three-quarters of the way between x ₍₁₎=1 and x ₍₂₎=3. The difference between x ₍₁₎ and x ₍₂₎ is 2, so

q_L = x ₍₁₎ + ¾(x ₍₂₎ – x ₍₁₎) = 1 + ¾ × 2 = 2.5.

The upper quartile is given by

So the upper quartile q_u is the number one-quarter of the way between x ₍₅₎=7 and x ₍₆₎=7. This is just the number 7 itself.

Having defined the quartiles, it is straightforward to define the measure of dispersion based on them: the interquartile range is the difference between the quartiles.