To find the median of this data set, follow these steps:

1. Arrange the data in ascending order:

   1, 2, 3, 5, 7, 8, 10, 15, 15, 22

2. Count the total number of data points:
   There are 10 numbers.

3. Identify the middle numbers:
   Since the number of data points is even, the median is the average of the two middle numbers. In this case, the two middle numbers are the 5th and 6th numbers in the ordered list.

4. Locate the 5th and 6th numbers:
   The 5th number is 7 and the 6th number is 8.

5. Calculate the average of the two middle numbers:

   $\text{Median} = \frac{7 + 8}{2} = \frac{15}{2} = 7.5$

Thus, the median is 7.5.

Would you like more details or have any further questions?

Here are 5 related questions:

1. What is the mode of this data set?
2. How would you calculate the mean of the same data set?
3. How does the size of a data set impact the median calculation?
4. How do we determine the range of a data set?
5. What is the effect of adding more numbers to the data set on the median?

Tip: When the number of data points is even, the median is always the average of the two middle numbers in the sorted data set.