The average marks of $28$ students in Mathematics was $5$. When $8$ students left the school, the average increased by $0.5$. What is the average of marks obtained by the students who left the school?

Step-by-step evaluation:
1. Calculate the initial total marks of all $28$ students:

$${\text{Total Marks}}_{28}=28\times 5=140$$

2. After $8$ students left, the number of remaining students is:

$$\text{Remaining Students}=28-8=20$$

3. The new average increases by $0.5$, making it $5+0.5=5.5$. Calculate the total marks of the remaining $20$ students:

$${\text{Total Marks}}_{20}=20\times 5.5=110$$

4. Find the total marks of the $8$ students who left:

$${\text{Total Marks}}_{\text{left}}=140-110=30$$

5. Find the average marks of the students who left:

$${\text{Average}}_{\text{left}}=\frac{30}{8}=3.75$$