1. **State the problem:** We need to find the mean, median, and mode of the paint orders given by the dot plot with gallons and their frequencies. 2. **List the data points and frequencies:** - 1 gallon: 5 dots - 2 gallons: 3 dots - 4 gallons: 1 dot - 5 gallons: 2 dots - 6 gallons: 1 dot - 7 gallons: 1 dot - 10 gallons: 1 dot 3. **Calculate the mean:** The mean is the sum of all values times their frequencies divided by the total number of data points. $$\text{Mean} = \frac{(1 \times 5) + (2 \times 3) + (4 \times 1) + (5 \times 2) + (6 \times 1) + (7 \times 1) + (10 \times 1)}{5 + 3 + 1 + 2 + 1 + 1 + 1}$$ Calculate numerator: $$= 5 + 6 + 4 + 10 + 6 + 7 + 10 = 48$$ Calculate denominator: $$= 5 + 3 + 1 + 2 + 1 + 1 + 1 = 14$$ So, $$\text{Mean} = \frac{48}{14} = \frac{\cancel{48}}{\cancel{14}} = 3.43 \text{ (rounded to nearest hundredth)}$$ 4. **Calculate the median:** The median is the middle value when data is ordered. Total data points = 14 (even number), so median is average of 7th and 8th values. List data in order: 1,1,1,1,1,2,2,2,4,5,5,6,7,10 The 7th value is 2 and the 8th value is 2. $$\text{Median} = \frac{2 + 2}{2} = 2$$ 5. **Calculate the mode:** The mode is the value with the highest frequency. From frequencies: - 1 gallon appears 5 times (highest) So, $$\text{Mode} = 1$$ **Final answers:** Mean = 3.43 Median = 2 Mode = 1