Q.Find $Q_1$, $Q_2$ and $Q_3$ for the data: $5, 8, 12, 15, 20, 25, 30$.

Data are ascending with $n = 7$, so $n + 1 = 8$; the quartile positions are whole numbers.

$Q_1 = 8$, $Q_2 = 15$, $Q_3 = 25$.

The seven values are already ascending, $n = 7$, $n + 1 = 8$.

$Q_1$: position $= \dfrac{1(8)}{4} = 2$ → the 2nd observation $= 8$, so $Q_1 = 8$.

$Q_2$: position $= \dfrac{2(8)}{4} = 4$ → the 4th observation $= 15$, so $Q_2 = 15$.

$Q_3$: position $= \dfrac{3(8)}{4} = 6$ → the 6th observation $= 25$, so $Q_3 = 25$.

Independent check. With $n = 7$ (odd), the median is the $\tfrac{7+1}{2} = 4$th value $= 15 = Q_2$ ✓, and $Q_1 \le Q_2 \le Q_3$ ($8 \le 15 \le 25$) ✓.

No interpolation is needed here because every position ($2, 4, 6$) is a whole number — a consequence of $n + 1 = 8$ being divisible by $4$. When $n + 1$ is a multiple of $4$, all three quartiles fall on actual observations.

Reordering slips: always confirm the data are ascending before reading off positions. Here they already are, but with unordered data the same positions would give wrong values.