1. **State the problem:** We need to find the mean number of refunds given in the summer and winter from 2015 to 2020 using the bar chart data, then determine if more refunds are given in winter than summer. 2. **Data from the bar chart:** - Summer refunds: 20, 15, 10, 15, 34, 38 - Winter refunds: 22, 10, 15, 18, 26, 29 3. **Formula for mean:** $$\text{Mean} = \frac{\text{Sum of values}}{\text{Number of values}}$$ 4. **Calculate mean for summer:** $$\text{Sum} = 20 + 15 + 10 + 15 + 34 + 38 = 132$$ $$\text{Number of years} = 6$$ $$\text{Mean summer} = \frac{132}{6}$$ Show canceling common factors: $$\frac{\cancel{132}}{\cancel{6}} = 22$$ 5. **Calculate mean for winter:** $$\text{Sum} = 22 + 10 + 15 + 18 + 26 + 29 = 120$$ $$\text{Number of years} = 6$$ $$\text{Mean winter} = \frac{120}{6}$$ Show canceling common factors: $$\frac{\cancel{120}}{\cancel{6}} = 20$$ 6. **Interpretation:** The mean number of refunds in summer is 22, and in winter is 20. 7. **Conclusion:** Since the mean refunds in summer (22) is greater than in winter (20), the hypothesis that more refunds are given in winter than summer is **not supported** by the data.