1. Problem: Janice recorded scores shown on the line plot and we must find the mean of the numbers. 2. Data: There is 1 observation at 1, 2 at 2, 4 at 3, 3 at 4, and 1 at 5. 3. Total observations: $n=1+2+4+3+1=11$. 4. Formula used: The mean is given by $$\bar{x}=\frac{\sum x_i}{n}$$ 5. Compute the sum of all scores: $$\sum x_i=1\cdot1+2\cdot2+4\cdot3+3\cdot4+1\cdot5=34$$ 6. Substitute into the formula to find the mean: $$\bar{x}=\frac{34}{11}\approx3.0909$$ 7. Final answer: The mean of the scores is $\frac{34}{11}\approx3.0909$.