Question

The observations 29, 32, 48, 50, x, x + 2, 72, 78, 84, 95 are arranged in ascending order. What is the value of x if the median of the data is 63?

Answer 1

If number of observations is even, then the median will be the average of $\left(\frac{n}{2}\right)$th and the $\left(\frac{n}{2}+1\right)$th observations.

In the given case, n = 10 $\Rightarrow \left(\frac{n}{2}\right)\mathrm{th}=5\mathrm{th}\mathrm{and}\left(\frac{n}{2}+1\right)\mathrm{th}=6\mathrm{th}$ observation.

Thus, $63=\frac{x+\left(x+2\right)}{2}$
$$\begin{gathered} \Rightarrow 126=2x+2 \\ \Rightarrow 124=2x \\ \Rightarrow x=62 \end{gathered}$$

Thus, the value of x is 62.