Q.Calculate the range and quartile deviation (Q.D.) of the following observations: 20, 25, 29, 30, 35, 39, 41, 48, 51, 60 and 70.

The values are already arranged in ascending order, so the largest is 70 and the smallest is 20, and with $n = 11$ the quartiles fall on whole-numbered positions.

Step 1 — Range. The largest value is $L = 70$ and the smallest is $S = 20$, so

Step 2 — Locate the quartiles. This is an individual (ungrouped) series with $n = 11$, and the values are already in ascending order.

$Q_1$ is the size of the $\dfrac{n+1}{4}\text{th} = \dfrac{11+1}{4} = 3\text{rd}$ value. The 3rd value is 29, so $Q_1 = 29$.

$Q_3$ is the size of the $\dfrac{3(n+1)}{4}\text{th} = \dfrac{3 \times 12}{4} = 9\text{th}$ value. The 9th value is 51, so $Q_3 = 51$.

Step 3 — Quartile deviation.

So the range of the data is 50 and the quartile deviation is 11. (Note that Q.D. is the average distance of the two quartiles from the median.)