To find the first quartile (Q1), follow these steps:

1. Sort the data in ascending order:
   5.3, 5.7, 9.0, 9.1, 9.6, 13.0, 15.7, 18.2, 19.1
   (The data is already sorted.)

2. Find the position of Q1 using the formula: $Q1 = \frac{n+1}{4}$ where $n$ is the total number of data points.

   • Here, $n = 9$. $Q1 = \frac{9+1}{4} = \frac{10}{4} = 2.5$ This means Q1 is located between the 2nd and 3rd data points.

3. Interpolate between the 2nd and 3rd data points:
   The 2nd data point is 5.7, and the 3rd data point is 9.0.
   Use interpolation: $Q1 = 5.7 + 0.5 \times (9.0 - 5.7)$ $Q1 = 5.7 + 0.5 \times 3.3 = 5.7 + 1.65 = 7.35$

So, the first quartile (Q1) is 7.35.

Would you like more details or have any questions?

Here are some related questions:

1. How do you calculate the second quartile (median) for the same data set?
2. What is the third quartile (Q3) of this data?
3. How do you calculate the interquartile range (IQR)?
4. Can you explain how outliers are detected using quartiles?
5. What are the differences between quartiles and percentiles?

Tip: Quartiles divide data into four equal parts, making them useful for understanding the spread of data.