Question

The following observations have been arranged in ascending order.

If the median of the data is $63$, find the value of $\mathrm{x}$.

$29,32,48,50,x,x+2,72,78,84,95$

Answer 1

Given:

The following observations have been arranged in ascending order. If the median of the data is $63$,

$29,32,48,50,x,x+2,72,78,84,95$

Number of observations ($\mathrm{n}$) $=10$

Median $=63$

Median, in statistics, is the middle value of the given list of data, when arranged in an order.

The number of observations is even, the median can be calculated as the average of the middlemost two elements.

Median $=\frac{{\left({\displaystyle \frac{\mathrm{n}}{2}}\right)}^{\mathrm{th}}\mathrm{observation}+{\left({\displaystyle \frac{\mathrm{n}}{2}}+1\right)}^{\mathrm{th}}\mathrm{observation}}{2}$

$\begin{array}{rcl}63& =& \frac{{\left({\displaystyle \frac{10}{2}}\right)}^{\mathrm{th}}\mathrm{observation}+{\left({\displaystyle \frac{10}{2}}+1\right)}^{\mathrm{th}}\mathrm{observation}}{2}\\ 63& =& \frac{5^{\mathrm{th}}\mathrm{observation}+6^{\mathrm{th}}\mathrm{observation}}{2}\\ 63& =& \frac{\left(\mathrm{x}\right)+\left(\mathrm{x}+2\right)}{2}\\ 126& =& 2x+2\\ \mathrm{x}& =& \frac{124}{2}\\ \mathrm{x}& =& 62\end{array}$

Hence, the value$\mathrm{x}$ is $62$.