The median of 1, 3, 4, 9, 10, x is 6. What is x?

Please find below the solution to the asked query:

We arrange given data in ascending order and get :

1 , 3 , 4 , x , 9 , 10  , Here we place ' x ' after 4 as given median is ' 6 '  that is greater than 4 but less than ' 9 ' .

We know if we have even number of data , So

Median  = $\frac{{\left({\displaystyle \frac{\mathrm{n}}{2}}\right)}^{\mathrm{th}} \mathrm{term} + {\left({\displaystyle \frac{\mathrm{n}}{2}} + 1\right)}^{\mathrm{th}} \mathrm{term}}{2}$ , Here number of data =  n  = 6 and also given median = 6 , So

$$\begin{gathered} \frac{{\left({\displaystyle \frac{6}{2}}\right)}^{\mathrm{th}} \mathrm{term} + {\left({\displaystyle \frac{6}{2}} + 1\right)}^{\mathrm{th}} \mathrm{term}}{2} = 6 \\ \Rightarrow \frac{3^{\mathrm{rd}} \mathrm{term} + 4^{\mathrm{th}} \mathrm{term}}{2} = 6 \\ \Rightarrow \frac{4 +x}{2} = 6 \\ \Rightarrow 4 +x= 12 \\ \mathbf{\Rightarrow }\mathit{x}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{8}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{(}\mathbf{ }\mathbf{Ans}\mathbf{ }\mathbf{)} \end{gathered}$$
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