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

1. **Total marks of all $28$ students:**
$${\text{Total Marks}}_{28}=28\times 5=140$$

2. Number of remaining students:

$$28-8=20\text{ students}$$

3. **New average marks of the remaining $20$ students:**

$$\text{New Average}=5+0.5=5.5$$

4. **Total marks of the remaining $20$ students:**

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

5. **Total marks of the $8$ students who left:**

$${\text{Total Marks}}_8=140-110=30$$

6. **Average marks of the $8$ students who left:**

$${\text{Average}}_8=\frac{30}{8}=3.75$$