If mean of 25, 29, 25, 32, 24 and X is 27, then what will be the value of median ?

Given mean of the 6 numbers $25, 29, 25, 32, 24, X$ is $27$: $\frac{135 + X}{6} = 27 \implies 135 + X = 162 \implies X = 27$. Arranging the 6 observations in ascending order gives $24, 25, 25, 27, 29, 32$. The Median is the average of the 3rd ($25$) and 4th ($27$) terms: $\frac{25 + 27}{2} = 26$.