To find the median, follow these steps:

1. Order the numbers in ascending order: $1, 2, 3, 5, 7, 8, 10, 15, 15, 22$

2. Determine if the dataset has an odd or even number of elements: There are 10 numbers, which is even.

3. Find the two middle numbers: Since there are 10 numbers, the middle numbers are the 5th and 6th numbers in the ordered set: $7 \, \text{and} \, 8$

4. Calculate the average of the two middle numbers: $\frac{7 + 8}{2} = \frac{15}{2} = 7.5$

So, the median of the dataset is 7.5.

Would you like further details or explanations on any step?

Here are 5 related questions to explore further:

1. What is the mode of the given dataset?
2. How would you calculate the mean of this dataset?
3. What is the range of these numbers?
4. How would the median change if you added another number to the dataset?
5. What is the importance of the median in statistical analysis?

Tip: When a dataset has an even number of elements, the median is the average of the two middle numbers.