(C) First,arrange the given data in ascending order:
$2, 5, 7, 7, 8, 10, 10, 10, 14, 17, 18, 24, 25, 27, 28, 48$
To find the mode,identify the value that occurs most frequently. The value $10$ appears $3$ times,which is more than any other value.
Therefore,the mode of the data $= 10$.
To find the median,count the total number of observations,$n = 16$ (which is even).
The median is the average of the $(\frac{n}{2})^{th}$ value and the $(\frac{n}{2} + 1)^{th}$ value.
Median $= \text{Average of } 8^{th} \text{ value and } 9^{th} \text{ value}$.
The $8^{th}$ value is $10$ and the $9^{th}$ value is $14$.
Median $= \frac{10 + 14}{2} = \frac{24}{2} = 12$.
Hence,the median is $12$ and the mode is $10$.