Question

If 10, 13, 15, 18, x + 1, x + 3, 30, 32, 35, 41 are ten observation in an ascending order with median 24, find the value of x.

Answer 1

10, 13, 15, 18, x+1, x+3, 30, 32, 35 and 41 are arranged in ascending order.
Median = 24
We have to find the value of x.
Here, n is 10, which is an even number.
Thus, we have:
$\mathrm{Median}=\mathrm{Mean}\mathrm{of}\left(\frac{n}{2}\right)\mathrm{th}\&\left(\frac{n}{2}+1\right)\mathrm{th}\mathrm{observations}$
$$\begin{gathered} \therefore \mathrm{Median}=\mathrm{Mean}\mathrm{of}\left(\frac{10}{2}\right)\mathrm{th}\&\left(\frac{10}{2}+1\right)\mathrm{th}\mathrm{observations} \\ =\mathrm{Mean}\mathrm{of}5\mathrm{th}\&6\mathrm{th}\mathrm{observations} \\ =\frac{1}{2}\left(x+1+x+3\right) \\ =\frac{1}{2}\left(2x+4\right) \\ =(x+2) \\ \mathrm{Given}: \\ \mathrm{Median}=24 \\ \Rightarrow x+2=24 \\ \Rightarrow x=22 \end{gathered}$$