The median of the numbers $11, 13, 15, 17,$ and $19$ is $15$.

To determine the median of a set of numbers, the first step is to arrange the numbers in ascending order. In this instance, the numbers are already in order: $11, 13, 15, 17,$ and $19$. The median is defined as the middle number in a list. Since there are five values in this list, which is an odd quantity, the middle number is the third one. Thus, the median is $15$.

In contrast, if the list contained an even number of elements, the median would be calculated by averaging the two middle numbers. For instance, if we had the numbers $11, 13, 15, 17, 19,$ and $21$, we would find the median by averaging $15$ and $17$, which is computed as:

However, since our current list has an odd number of elements, we simply select the middle number, which is $15$.

Understanding the median is crucial because it provides a measure of central tendency that remains unaffected by extremely high or low values, unlike the mean. This characteristic makes the median a valuable statistic in various real-world contexts, such as analyzing income data or exam scores, where outliers can significantly distort the results.