Using Statement-I alone: Statement-I provides the highest marks ($70$) and the lowest marks ($50$) but does not give information about the total number of students or their individual marks. Hence, it is not sufficient to determine the number of students in the class. Therefore, Statement-I alone is insufficient.

Using Statement-II alone: Statement-II tells us that excluding the highest and lowest marks does not change the average, which means the average of the remaining marks is also $60$. However, this alone does not provide enough information to calculate the total number of students. Therefore, Statement-II alone is insufficient.

Combining Statement-I and Statement-II: From Statement-II, we know that excluding the highest ($70$) and lowest ($50$) marks does not change the average, so the average of the remaining marks is still $60$. Let the number of students in the class be $n$, and the total sum of marks be $S$. The average marks are given by:

$S/n = 60$, so $S = 60n$.

After excluding the highest and lowest marks, the sum of the remaining marks is $(S - 70 - 50) = S - 120$, and the number of students is $(n - 2)$.

Thus, the new average is:

$(S - 120) / (n - 2) = 60$.

Substituting $S = 60n$:

$(60n - 120) / (n - 2) = 60$.

Simplifying:

$60n - 120 = 60(n - 2)$,

$60n - 120 = 60n - 120$.

This equation holds true for any value of $n$, indicating that no specific number of students can be determined. Therefore, both statements together still do not give a unique answer.