Question

The following observations are arranged in ascending order. If the median of the data is 17 find x if the observations are 6, 8, 9, 15, x, x + 2, 21, 22, 25, 29.

Answer 1

The given observations are:
6, 8, 9, 15, x, x + 2, 21, 22, 25, 29
Here,
n =10
Now,
$$\begin{gathered} \mathrm{Median}=\frac{\left({\displaystyle \frac{n}{2}}\right)\mathrm{th}\mathrm{term}+\left({\displaystyle \frac{n+2}{2}}\right)\mathrm{th}\mathrm{term}}{2} \\ \Rightarrow 17=\frac{\left({\displaystyle \frac{10}{2}}\right)\mathrm{th}\mathrm{term}+\left({\displaystyle \frac{12}{2}}\right)\mathrm{th}\mathrm{term}}{2} \\ \Rightarrow 17=\frac{5\mathrm{th}\mathrm{term}+6\mathrm{th}\mathrm{term}}{2} \\ \Rightarrow 17=\frac{x+x+2}{2} \\ \Rightarrow 17=\frac{2x+2}{2} \\ \Rightarrow 17=\frac{2\left(x+1\right)}{2} \\ \Rightarrow 17=x+1 \\ \Rightarrow x=17-1=16 \end{gathered}$$