1. **State the problem:** We want to find the mean number of pictures painted based on the given frequency data. 2. **Data interpretation:** The horizontal axis shows the number of pictures painted: 1, 2, 3, 4, 5, 6. The frequencies (number of Xs) for each are: - 1 picture: 4 times - 2 pictures: 5 times - 3 pictures: 0 times (no Xs) - 4 pictures: 1 time - 5 pictures: 1 time - 6 pictures: 2 times 3. **Formula for mean:** $$\text{Mean} = \frac{\sum (\text{value} \times \text{frequency})}{\sum \text{frequency}}$$ 4. **Calculate numerator (sum of value times frequency):** $$1 \times 4 + 2 \times 5 + 3 \times 0 + 4 \times 1 + 5 \times 1 + 6 \times 2 = 4 + 10 + 0 + 4 + 5 + 12 = 35$$ 5. **Calculate denominator (total frequency):** $$4 + 5 + 0 + 1 + 1 + 2 = 13$$ 6. **Calculate mean:** $$\text{Mean} = \frac{35}{13} \approx 2.69$$ **Final answer:** The mean number of pictures painted is approximately $2.69$.