Numbers 50, 42, 35, 2x + 10, 2x – 8, 12, 11, 8 are written in descending order and their median is 25, find x.
Question:

Numbers 50, 42, 35, 2x + 10, 2x – 8, 12, 11, 8 are written in descending order and their median is 25, find x.

Solution:

Given the number of observation, n = 8

$\therefore$ Median $=\frac{\overline{\overline{2}}^{\text {th }} \text { value }+\left(\frac{\mathrm{n}}{2}+1\right)^{\text {th }} \text { value }}{2}$

$=\frac{\frac{8^{\text {th }}}{2} \text { value }+\left(\frac{8}{2}+1\right)^{\text {th }} \text { value }}{2}$

$=\frac{4^{\text {th }} \text { value }+5^{\text {th }} \text { value }}{2}$

$=\frac{2 x+10+2 x-8}{2}$

= 2x + 1

Given Median = 25

∴ 2x + 1 = 25

⇒ 2x = 24

⇒ x = 12