1. **State the problem:** We need to identify which mistake Katie made in her stem-and-leaf diagram for the caterpillar lengths. 2. **List given lengths:** The lengths are: $$56, 69, 74, 52, 81, 87, 81, 53, 70, 52, 55, 68, 70, 86, 81$$ 3. **Count and categorize lengths by tens digit (stem):** - Stem 5 (50-59): $52, 52, 53, 55, 56$ (5 values) - Stem 6 (60-69): $68, 69$ (2 values) - Stem 7 (70-79): $70, 70, 74$ (3 values) - Stem 8 (80-89): $81, 81, 81, 86, 87$ (5 values) 4. **Compare with stems and leaves in the diagram:** - Stem 5 leaves shown: $2, 2, 3, 5, 6$ (5 values) [matches data] - Stem 6 leaves shown: $8, 9$ (2 values) [matches data] - Stem 7 leaves shown: $0, 4$ (2 values) [data has 3 values: 70, 70, 74] - Stem 8 leaves shown: $1, 1, 1, 6, 7$ (5 values) [data has $81, 81, 81, 86, 87$] 5. **Find the discrepancy:** The stem 7 row is missing one leaf for the second 70. It should have two zeros to represent two 70s. 6. **Check the key:** Katie did not include a key in her diagram. 7. **Check for extra length:** All lengths in the stem-and-leaf diagram correspond to lengths in the list; none are extras. 8. **Check if any row is missing:** All stems 5, 6, 7, and 8 appear. **Conclusion:** Katie missed a length in the stem 7 row (one 70 is missing) and omitted the key. Since the question asks for which mistake Katie made (singular), the primary mistake is: **Missed a length** (the second 70 under stem 7).