For the nine values 12, 15, 18, 20, 22, 25, 28, 30, 35 (already in ascending order) find the quartile deviation, taking the quartiles at positions (n + 1)/4 and 3(n + 1)/4.

Here n = 9, so Q1 sits at position (9 + 1)/4 = 2.5, halfway between the 2nd and 3rd values: Q1 = (15 + 18)/2 = 16.5. Q3 sits at position 3(9 + 1)/4 = 7.5, halfway between the 7th and 8th: Q3 = (28 + 30)/2 = 29. The quartile deviation is HALF the interquartile range, so it is (29 − 16.5)/2 = 12.5/2 = 6.25. Stopping at 12.5 gives the interquartile range and forgets the halving; 16.5 is Q1 by itself and 22 is the median.