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
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
Solution:
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 $\frac{10}{2}$ i.e., $5^{\text {th }}$ and $\frac{10}{2}+1$ i.e., $6^{\text {th }}$ observation.
Therefore, median of data $=\frac{5^{\text {th }} \text { observation }+6^{\text {th }} \text { observation }}{2}$
$\Rightarrow 63=\frac{x+x+2}{2}$
$\Rightarrow 63=\frac{2 x+2}{2}$
$\Rightarrow 63=x+1$
$\Rightarrow x=62$
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 $\frac{10}{2}$ i.e., $5^{\text {th }}$ and $\frac{10}{2}+1$ i.e., $6^{\text {th }}$ observation.
Therefore, median of data $=\frac{5^{\text {th }} \text { observation }+6^{\text {th }} \text { observation }}{2}$
$\Rightarrow 63=\frac{x+x+2}{2}$
$\Rightarrow 63=\frac{2 x+2}{2}$
$\Rightarrow 63=x+1$
$\Rightarrow x=62$