Find the median and mean of the data set 44, 4, 27, 5

1. Order the data set: To find the median, we first arrange the given numbers in ascending order: $4, 5, 27, 44$.

2. Find the median: The median is the middle value of a data set. Since there is an even number of values ($n=4$), the median is the average of the two middle numbers. The middle numbers are $5$ and $27$.
$$\text{Median} = \frac{5 + 27}{2} = \frac{32}{2} = 16$$

3. Find the mean: The mean is the sum of all values divided by the number of values in the set.
$$\text{Sum} = 4 + 5 + 27 + 44 = 80$$
$$\text{Mean} = \frac{\text{Sum}}{\text{Number of values}} = \frac{80}{4} = 20$$