1. **State the problem:** We have a dataset of 7 students with their GPA values: 3.5, 3.1, 3.2, 4.0, 3.6, 3.2, 2.7. 2. We want to find how the mean and median GPA change if a new student with GPA 1.5 is added. 3. **Calculate the original mean GPA:** $$\text{mean} = \frac{3.5 + 3.1 + 3.2 + 4.0 + 3.6 + 3.2 + 2.7}{7} = \frac{23.3}{7} \approx 3.33$$ 4. **Calculate the new mean GPA with the added student:** $$\text{new mean} = \frac{23.3 + 1.5}{7 + 1} = \frac{24.8}{8} = 3.1$$ 5. **Calculate the original median GPA:** Sort the GPAs: 2.7, 3.1, 3.2, 3.2, 3.5, 3.6, 4.0 The median is the middle value (4th value): $3.2$ 6. **Calculate the new median GPA with the added student:** Add 1.5 and sort: 1.5, 2.7, 3.1, 3.2, 3.2, 3.5, 3.6, 4.0 With 8 values, median is average of 4th and 5th values: $$\text{median} = \frac{3.2 + 3.2}{2} = 3.2$$ 7. **Summary:** - Mean GPA decreases from approximately $3.33$ to $3.1$ due to the low GPA of the new student. - Median GPA remains unchanged at $3.2$ because the middle values are the same after adding the new GPA. Thus, adding a student with GPA 1.5 lowers the mean but does not affect the median.