1. **State the problem:** Find the 14th percentile, $P_{14}$, from the given data set. 2. **Recall the formula for the percentile position:** $$ L = \frac{P}{100} \times (n + 1) $$ where $P$ is the percentile (14 here) and $n$ is the number of data points. 3. **Count the number of data points:** There are 39 data points. 4. **Calculate the position $L$:** $$ L = \frac{14}{100} \times (39 + 1) = 0.14 \times 40 = 5.6 $$ 5. **Interpret $L=5.6$:** The 14th percentile lies between the 5th and 6th data points. 6. **Identify the 5th and 6th data points:** Sorted data points are: 1: 10 2: 11 3: 11.5 4: 11.6 5: 14.3 6: 14.7 7. **Interpolate to find $P_{14}$:** $$ P_{14} = x_5 + (L - 5)(x_6 - x_5) = 14.3 + (5.6 - 5)(14.7 - 14.3) = 14.3 + 0.6 \times 0.4 = 14.3 + 0.24 = 14.54 $$ 8. **Final answer:** $$ P_{14} = 14.54 $$ This means 14% of the data falls below approximately 14.54.