From the following data; find :

(i) Median

(ii) Upper quartile

(iii) Inter-quartile range.

25, 10, 40, 88, 45, 60, 77, 36, 18, 95, 56, 65, 7, 0, 38 and 83

(i) Set of numbers in ascending order :

0, 7, 10, 18, 25, 36, 38, 40, 45, 56, 60, 65, 77, 83, 88, 95.

Here, n = 16, which is even.

By formula,

$\text{Median }= \dfrac{\dfrac{n}{2} \text{ th term} + \Big(\dfrac{n}{2} + 1\Big) \text{ th term}}{2} \\[1em] = \dfrac{\dfrac{16}{2} \text{th term} + \Big(\dfrac{16}{2} + 1\Big)\text{ th term}}{2} \\[1em] = \dfrac{8\text{ th term} + 9\text{ th term}}{2} \\[1em] = \dfrac{40 + 45}{2} \\[1em] = \dfrac{85}{2} \\[1em] = 42.5$

Hence, median = 42.5

(ii) By formula,

Upper quartile = $\dfrac{3n}{4}$ th term

= $\dfrac{3 \times 16}{4} = \dfrac{48}{4}$ = 12th term

= 65.

Hence, upper quartile = 65.

(iii) By formula,

Lower quartile = $\dfrac{n}{4}$ th term

= $\dfrac{16}{4}$ = 4th term

= 18.

Inter quartile range = Upper quartile - Lower quartile

= 65 - 18

= 47.

Hence, inter quartile range = 47.