1. **State the problem:** We are given the number of pieces in each puzzle and their frequencies: 20 pieces (2 puzzles), 30 pieces (1 puzzle), 50 pieces (3 puzzles), 80 pieces (1 puzzle), and 100 pieces (1 puzzle). 2. **Formula for the mean:** The mean (average) is calculated by $$\text{mean} = \frac{\sum (\text{value} \times \text{frequency})}{\sum \text{frequency}}$$ 3. **Calculate the total number of puzzles:** $$2 + 1 + 3 + 1 + 1 = 8$$ 4. **Calculate the sum of pieces:** $$20 \times 2 + 30 \times 1 + 50 \times 3 + 80 \times 1 + 100 \times 1 = 40 + 30 + 150 + 80 + 100 = 400$$ 5. **Calculate the mean:** $$\text{mean} = \frac{400}{8} = 50$$ 6. **Interpretation:** The mean describes the center of the distribution because it represents the average number of pieces per puzzle. **Final answer:** The mean of the data is 50 pieces. It describes the center of the distribution.