Question

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

$29,32,48,50,\mathrm{x},\mathrm{x}+2,72,78,84,95$

Answer 1

Find the required value:

Given data is $29,32,48,50,\mathrm{x},\mathrm{x}+2,72,78,84,95$

The median of the data is $63$.

Since data numbers are even.

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

$$\begin{gathered} \mathrm{Median}=\frac{5\mathrm{th}\mathrm{term}+6\mathrm{th}\mathrm{term}}{2} \\ 63=\frac{\mathrm{x}+\mathrm{x}+2}{2} \\ 2\times 63=2\mathrm{x}+2 \\ 126=2\mathrm{x}+2 \\ 126-2=2\mathrm{x} \\ 124=2\mathrm{x} \\ \mathrm{x}=\frac{124}{2}=62 \end{gathered}$$

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