The following graph shows the performance of students in an exam. The marks scored by every student are a multiple of five. The $j^{th}$-percentile $u^*$ for a discrete data $x_1,x_2,…,x_n$ is defined as follows. Let $x_{(1)},x_{(2)},\dots ,x_{(n)}$ be the ordering of the data in ascending order. Let $t=\frac{j-n}{100}$ and let $k$ be an integer such that $k\leq t< (k+1)$ and let $s=t-k.$ Then $u^* =x_{(k)} +s*(x_{(k+1)}-x_{(k)}).$ Here, $x_{(n+1)}$ is defined to be $x_{(n)}$.
Based on the information presented in the graph, answer the following questions.
- Compute the $10^{th}$ percentile of marks.
- Is the median score higher than the mean score?
