The average of marks obtained in an examination by $8$ students was $5.1$ and by $9$ other students was $6.8$. The average marks of the $17$ students were:

To find the combined average of all $17$ students, we use the formula for weighted average:
$$\text{Combined Average}=\frac{\text{Total marks of all students}}{\text{Total number of students}}$$

1. Total marks of the first group of $8$ students:

$${\text{Sum}}_1=8\times 5.1=40.8$$

2. Total marks of the second group of $9$ students:

$${\text{Sum}}_2=9\times 6.8=61.2$$

3. Combined sum of marks for all $17$ students:

$$\text{Total Sum}=40.8+61.2=102$$

4. Combined average:

$$\text{Average}=\frac{102}{17}=6.0$$

Hence, the average marks of the $17$ students are $6.0$.