1. **Stating the problem:** We are given the least mark, median, lower quartile, interquartile range, and range, and we need to find the upper quartile and the highest mark. 2. **Given data:** - Least mark = 77 - Median = 82 - Lower quartile = 80 - Interquartile range (IQR) = 4 - Range = 10 3. **Formulas and rules:** - The interquartile range is defined as $$\text{IQR} = Q_3 - Q_1$$ where $Q_3$ is the upper quartile and $Q_1$ is the lower quartile. - The range is defined as $$\text{Range} = \text{Highest mark} - \text{Least mark}$$ 4. **Calculate the upper quartile:** $$Q_3 = Q_1 + \text{IQR} = 80 + 4 = 84$$ 5. **Calculate the highest mark:** $$\text{Highest mark} = \text{Least mark} + \text{Range} = 77 + 10 = 87$$ **Final answers:** - Upper quartile = 84 - Highest mark = 87