To find the median of a data set, we first need to order the numbers from smallest to largest, then find the middle value.

Original Data Set:

$17, 40, 39, 13, 32, 19, 10, 16, 6, 24, 21, 26, 1, 22$

Step 1: Sort the Numbers in Ascending Order:

$1, 6, 10, 13, 16, 17, 19, 21, 22, 24, 26, 32, 39, 40$

Step 2: Find the Median

There are 14 numbers in total. Since the number of elements is even, the median is the average of the two middle values. The middle values in this case are the 7th and 8th numbers:

$19 \, \text{and} \, 21$

Median Calculation:

$\text{Median} = \frac{19 + 21}{2} = 20$

Thus, the median of the given data set is 20.

Would you like further details or have any questions about this solution?

Here are some additional related questions to think about:

1. How would you find the mode of this data set?
2. How would you calculate the mean of this data set?
3. What happens if there is an odd number of data points? How is the median calculated then?
4. Can you describe a situation where the median is more useful than the mean?
5. How would you identify outliers in this data set?

Tip: For a large data set, sorting the numbers can be time-consuming, so techniques like using a frequency distribution can help speed up the process of finding the median.