Question

Following 10 observations are arranged in ascending order as follows.

2, 3, 5, 9, x + 1, x + 3, 14, 16, 19, 20

If the median of the data is 11, find the value of x

Answer 1

Given:

The 10 observations are arranged in ascending order as follows:

2, 3, 5, 9, x + 1, x + 3, 14, 16, 19, 20

Since, the median of the data is 11.

As, the number of observations = 10, which is an even number.

$$\begin{gathered} \Rightarrow \mathrm{Median}=11 \\ \Rightarrow \frac{1}{2}\left[\left(\frac{10}{2}\right)\mathrm{th}\mathrm{observation}+\left(\frac{10}{2}+1\right)\mathrm{th}\mathrm{observation}\right]=11 \\ \Rightarrow \frac{1}{2}\left[5\mathrm{th}\mathrm{observation}+6\mathrm{th}\mathrm{observation}\right]=11 \\ \Rightarrow \frac{1}{2}\left[x+1+x+3\right]=11 \\ \Rightarrow 2\mathrm{x}+4=2\times 11 \\ \Rightarrow 2\mathrm{x}=22-4 \\ \Rightarrow \mathrm{x}=\frac{18}{2}=9 \end{gathered}$$

So, the value of x is 9.