Question

The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x.
29, 32, 48, 50, x, x + 2, 72, 78, 84, 95.
[2 Marks]

Answer 1

It can be observed that the total number of observations in the given data is 10 (even number).

Therefore, the median of this data will be the mean of ${\frac{10}{2}}^{th}$ and $(\frac{10}{2}+1{)}^{th}$ observation, i.e. mean of $5^{th}$ and $6^{th}$ observation.

Median = $\frac{\text{5th observation + 6th observation}}{2}$

$\Rightarrow 63=\frac{x+x+2}{2}$ [1 Mark]

$\Rightarrow 63=\frac{2x+2}{2}$

$\Rightarrow 63=x+1$

$\Rightarrow x=62$ [1 Mark]