Question: Find the lower quartile of the data values below.
41.3, 11.8, 64.9, 29.5, 59, 5.9, 23.6, 47.2, 17.7, 35.4, 53.1
use (n+1) formula
Write the final answer only. Enter digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) and decimal point (.) only. DO NOT enter any letters (A-Z / a-z).
1. **State the problem:** Find the lower quartile (Q1) of the data set: $41.3, 11.8, 64.9, 29.5, 59, 5.9, 23.6, 47.2, 17.7, 35.4, 53.1$ using the formula $Q1 = \text{value at position } \frac{1}{4}(n+1)$ where $n$ is the number of data points.
2. **Count the data points:** There are $n=11$ values.
3. **Order the data from smallest to largest:**
$$5.9, 11.8, 17.7, 23.6, 29.5, 35.4, 41.3, 47.2, 53.1, 59, 64.9$$
4. **Calculate the position of Q1:**
$$Q1 = \frac{1}{4}(n+1) = \frac{1}{4}(11+1) = \frac{1}{4} \times 12 = 3$$
5. **Interpret the position:** The lower quartile is the value at the 3rd position in the ordered list.
6. **Find the value at position 3:** The 3rd value is $17.7$.
**Final answer:**
$$17.7$$