The median is the middle value of a data set when the numbers are arranged in order from smallest to largest. If the data set has an odd number of values, the median is the middle number. If the data set has an even number of values, the median is the average of the two middle numbers.

Let's find the median for your set of numbers:
5, 8, 15, 7, 10, 22, 3, 1, 15

Step-by-step process:

1. Arrange the numbers in ascending order: 1, 3, 5, 7, 8, 10, 15, 15, 22

2. Identify the number of values: There are 9 numbers, which is an odd number.

3. Find the middle number: The middle value is the 5th number in this ordered list.

   Median = 8

So, the median of this data set is 8.

Would you like more details on medians or any further clarifications?

Here are 5 related questions to expand your understanding:

1. How does the median differ from the mean?
2. What happens if the data set has an even number of values?
3. Can the median be affected by outliers?
4. How is the median used in real-life applications?
5. What are the advantages of using the median over other measures of central tendency?

Tip: When arranging numbers for median, double-check the order to avoid errors, especially with large data sets.