Question

The following observations are arranged in ascending order:
26, 29, 42, 53, x, x + 2, 70, 75, 82, 93.
If the median is 65, find the value of x.

Answer 1

Arranging the given data in ascending order:
26, 29, 42, 53, x, x + 2, 70, 75, 82, 93

Number of terms = 10 (even)

$$\begin{gathered} \therefore \mathrm{Median}=\mathrm{mean}\mathrm{of}\left[{\left(\frac{n}{2}\right)}^{\mathrm{th}}\mathrm{term}\mathrm{and}{\left(\frac{n}{2}+1\right)}^{\mathrm{th}}\mathrm{term}\right] \\ \Rightarrow 65=\mathrm{mean}\mathrm{of}\left[{\left(\frac{10}{2}\right)}^{\mathrm{th}}\mathrm{term}\mathrm{and}{\left(\frac{10}{2}+1\right)}^{\mathrm{th}}\mathrm{term}\right] \\ \Rightarrow 65=\mathrm{mean}\mathrm{of}\left[{\left(5\right)}^{\mathrm{th}}\mathrm{term}\mathrm{and}{\left(6\right)}^{\mathrm{th}}\mathrm{term}\right] \\ \Rightarrow 65=\mathrm{mean}\mathrm{of}\left[x\mathrm{and}x+2\right] \\ \Rightarrow 65=\frac{x+x+2}{2} \\ \Rightarrow 65\times 2=2x+2 \\ \Rightarrow 130=2x+2 \\ \Rightarrow 2x=130-2 \\ \Rightarrow 2x=128 \\ \Rightarrow x=64 \end{gathered}$$

Hence, the value of x is 64.