Question

The observations in the data set given below are 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

• A. 60
• B. 61
• C. 62
• D. 63

Answer 1

The correct option is C 62

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 $\left(\frac{10}{2}\right)\text{th observation}$ and $(\frac{10}{2}+1)\text{th observation}$.

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

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

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

$\Rightarrow 63=x+1$

$\Rightarrow x=62$