To find the first quartile (Q1) for the given list of numbers, we will follow these steps:

1. Arrange the numbers in ascending order:

15, 20, 22, 28, 32, 43, 45, 59, 61, 66, 72, 75, 83, 85, 88

2. Find the position of Quartile 1 (Q1):

The first quartile (Q1) is the value at the 25th percentile, which separates the lowest 25% of the data from the rest.

To find the position, use the formula for quartiles: $Q1 = \dfrac{(n+1)}{4}$ where $n$ is the total number of data points.

In this case, $n = 15$, so: $Q1 = \dfrac{(15+1)}{4} = \dfrac{16}{4} = 4$

This means the first quartile is the 4th number in the ordered list.

3. Find the value at the 4th position:

The 4th number in the ordered list is 28.

Therefore, Quartile 1 (Q1) = 28.

Would you like further details or have any questions?

Here are 5 related questions for deeper understanding:

1. How do you calculate other quartiles from a data set?
2. How do quartiles help in understanding data distribution?
3. What are some differences between quartiles and percentiles?
4. How do you calculate the interquartile range (IQR)?
5. Can you use quartiles in larger data sets differently?

Tip: Quartiles are useful in identifying outliers, as values outside of 1.5 times the interquartile range (IQR) from the quartiles are often considered outliers.