Question

The following observations are arranged in ascending order: $26,29,42,53,x,x+2,70,75,82,93$. If the median is $65$, find the value of $x$.

Answer 1

Find the value of $x$:

The observations are arranged in ascending order: $26,29,42,53,x,x+2,70,75,82,93$.

Let $n$ be the number of observations, $n=10$

Median is $65$

When $n$ is even, then median $=\frac{1}{2}\left[{\left(\frac{n}{2}\right)}^{th}term+{\left(\frac{n}{2}+1\right)}^{th}term\right]$

$\therefore \frac{1}{2}\left[{\left(\frac{10}{2}\right)}^{th}term+{\left(\frac{10}{2}+1\right)}^{th}term\right]=65$

$\Rightarrow \frac{1}{2}\left[5^{th}term+6^{th}term\right]=65$

$\Rightarrow \frac{1}{2}\left[x+x+2\right]=65$

$\Rightarrow \frac{1}{2}\left[2x+2\right]=65$

$\Rightarrow \frac{2}{2}\left[x+1\right]=65$

$\Rightarrow x=65-1=64$

Therefore, the value of $x$ is $64$