The marks obtained by $\displaystyle 80$ students of class X in a mock test of Mathematics are given below in the table. Find median and the mode of the data :

Marks & Number of Students & Class Interval & \(\displaystyle f\) & Cf $\displaystyle 0$ and above & $\displaystyle 80$ & $\displaystyle 0$-$\displaystyle 10$ & $\displaystyle 3$ & $\displaystyle 3$ $\displaystyle 10$ and above & $\displaystyle 77$ & $\displaystyle 10$-$\displaystyle 20$ & $\displaystyle 5$ & $\displaystyle 8$ $\displaystyle 20$ and above & $\displaystyle 72$ & $\displaystyle 20$-$\displaystyle 30$ & $\displaystyle 7$ & $\displaystyle 15$ $\displaystyle 30$ and above & $\displaystyle 65$ & $\displaystyle 30$-$\displaystyle 40$ & $\displaystyle 10$ & $\displaystyle 25$ $\displaystyle 40$ and above & $\displaystyle 55$ & $\displaystyle 40$-$\displaystyle 50$ & $\displaystyle 12$ & $\displaystyle 37$ $\displaystyle 50$ and above & $\displaystyle 43$ & $\displaystyle 50$-$\displaystyle 60$ & $\displaystyle 15$ & $\displaystyle 52$ $\displaystyle 60$ and above & $\displaystyle 28$ & $\displaystyle 60$-$\displaystyle 70$ & $\displaystyle 12$ & $\displaystyle 64$ $\displaystyle 70$ and above & $\displaystyle 16$ & $\displaystyle 70$-$\displaystyle 80$ & $\displaystyle 6$ & $\displaystyle 70$ $\displaystyle 80$ and above & $\displaystyle 10$ & $\displaystyle 80$-$\displaystyle 90$ & $\displaystyle 2$ & $\displaystyle 72$ $\displaystyle 90$ and above & $\displaystyle 8$ & $\displaystyle 90$-$\displaystyle 100$ & $\displaystyle 8$ & $\displaystyle 80$ Total & & & $\displaystyle 80$ &\[n=80 \Rightarrow \frac{n}{2}=40 \] ∴ $\displaystyle 50$-$\displaystyle 60$ is the median class \[\begin{aligned} \text { Median } & =50+\left(\frac{40-37}{15}\right) \times 10 \\ & =50+2=52 \end{aligned} \] \(\displaystyle 50-60\) is the modal class \[\begin{aligned} \text { Mode }= & 50+\left(\frac{15-12}{2 \times 15-12-12}\right) \times 10 \\ & =50+5=55 \end{aligned} \]