1. **Problem 5a:** Show that the test score of 25 is not an outlier given the lower quartile (Q1) = 62 and upper quartile (Q3) = 88. 2. **Formula and rule:** To check for outliers, use the Interquartile Range (IQR) method: $$\text{IQR} = Q3 - Q1 = 88 - 62 = 26$$ Outliers are values below $$Q1 - 1.5 \times IQR$$ or above $$Q3 + 1.5 \times IQR$$. 3. **Calculate lower and upper bounds:** $$\text{Lower bound} = 62 - 1.5 \times 26 = 62 - 39 = 23$$ $$\text{Upper bound} = 88 + 1.5 \times 26 = 88 + 39 = 127$$ 4. **Check the score 25:** Since $$25 > 23$$ and $$25 < 127$$, the score 25 is within the bounds and therefore **not an outlier**. 5. **Problem 5b:** Compare the morning and evening classes using the box and whisker diagrams. 6. **Aspect supporting the researcher's opinion:** The evening class has a higher median (center of the box) approximately between 75 and 90, while the morning class median is between 62 and 88. This suggests the evening class generally scored higher. 7. **Aspect countering the researcher's opinion:** The morning class has a wider range of scores (from 25 to 98) compared to the evening class (about 50 to 98), indicating more variability and some lower scores in the morning class, which might affect overall performance. **Final answers:** - The score 25 is not an outlier because it lies within the calculated bounds. - The evening class median is higher, supporting better performance. - The morning class has a wider score range, which may counter the opinion of better performance in the evening class.