1. **Problem Statement:** Find the 10th percentile of the given data set. 2. **Understanding Percentiles:** The $p$th percentile is the value below which $p\%$ of the data falls. To find the 10th percentile, we need to determine the position of the value that separates the lowest 10% of the data. 3. **Data Preparation:** The data is given in a 5 by 6 table, so there are $5 \times 6 = 30$ data points in total. 4. **Calculate the Position:** The position $P$ of the 10th percentile in an ordered data set of size $n$ is given by: $$P = \frac{p}{100} \times (n + 1)$$ Substituting $p=10$ and $n=30$: $$P = \frac{10}{100} \times (30 + 1) = 0.1 \times 31 = 3.1$$ 5. **Interpret the Position:** The 10th percentile lies between the 3rd and 4th data points in the ordered list. 6. **List the Data in Order:** The data in ascending order (row-wise) is: $$5, 15, 15, 15, 20, 31, 32, 32, 36, 36, 40, 47, 50, 55, 58, 60, 61, 63, 66, 68, 71, 73, 73, 75, 79, 80, 81, 84, 87, 90$$ 7. **Find the 3rd and 4th Data Points:** The 3rd data point is 15, and the 4th data point is 15. 8. **Interpolate if Needed:** Since both values are the same, the 10th percentile is 15. **Final Answer:** The 10th percentile of the data is $15$.