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Answer :
First, we arrange the ages in increasing order:
$$
51,\ 54,\ 57,\ 57,\ 57,\ 57,\ 58,\ 61,\ 61,\ 68.
$$
Since there are 10 values (an even number), the median is the average of the two middle numbers. Here, the middle numbers are the 5th and 6th numbers in the sorted list.
The 5th number is $57$, and the 6th number is also $57$. Therefore, the median is calculated as:
$$
\text{Median} = \frac{57 + 57}{2} = \frac{114}{2} = 57.
$$
Thus, the median of the ages is $\boxed{57}$.
$$
51,\ 54,\ 57,\ 57,\ 57,\ 57,\ 58,\ 61,\ 61,\ 68.
$$
Since there are 10 values (an even number), the median is the average of the two middle numbers. Here, the middle numbers are the 5th and 6th numbers in the sorted list.
The 5th number is $57$, and the 6th number is also $57$. Therefore, the median is calculated as:
$$
\text{Median} = \frac{57 + 57}{2} = \frac{114}{2} = 57.
$$
Thus, the median of the ages is $\boxed{57}$.
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