Question

If the numbers 2, 3, x, x+2, 11, 17 are in ascending order and their median is 9,then find the value of 3x+1.

Answer 1

Dear Student,

$$\begin{gathered} Numberofobservations=6 \\ Median(inthecaseofevennumberofobservations)=\frac{({\displaystyle \frac{n}{2}}{)}^{th}term+({\displaystyle \frac{n}{2}}+1{)}^{th}term}{2} \\ Given:Median=9 \\ So,9=\frac{({\displaystyle \frac{6}{2}}{)}^{th}term+({\displaystyle \frac{6}{2}}+1{)}^{th}term}{2} \\ \Rightarrow 9=\frac{3^{rd}term+4^{th}term}{2} \\ \Rightarrow 9=\frac{x+x+2}{2} \\ \Rightarrow 9=\frac{2x+2}{2} \\ \Rightarrow 9=\frac{2(x+1)}{2} \\ \Rightarrow 9=x+1 \\ \Rightarrow x=9-1 \\ \Rightarrow x=8 \\ \mathbf{3}\mathit{x}\mathbf{}\mathbf{+}\mathbf{}\mathbf{1}\mathbf{}\mathbf{=}\mathbf{}\mathbf{3}\mathbf{\left(}\mathbf{8}\mathbf{\right)}\mathbf{}\mathbf{+}\mathbf{}\mathbf{1}\mathbf{}\mathbf{=}\mathbf{}\mathbf{24}\mathbf{}\mathbf{+}\mathbf{}\mathbf{1}\mathbf{}\mathbf{=}\mathbf{}\mathbf{25} \end{gathered}$$

Regards