1. **Stating the problem:** We have a set of test scores from a class: 80, 82, 72, 90, 100, 95, 88, 75, 75, 85, 95, 85, 85, 78, 92. 2. **Real-world situation:** Imagine a teacher who gave a math test to 15 students. These numbers represent the scores each student received on the test. 3. **Using the data:** The teacher wants to understand how the class performed overall by calculating key statistics: mean (average), median (middle score), mode (most frequent score), range (difference between highest and lowest), and interquartile range (spread of the middle 50% of scores). 4. **Formulas and explanations:** - Mean: $$\text{Mean} = \frac{\text{Sum of all scores}}{\text{Number of scores}}$$ - Median: The middle value when all scores are ordered. - Mode: The score that appears most frequently. - Range: $$\text{Range} = \text{Maximum score} - \text{Minimum score}$$ - Interquartile Range (IQR): $$\text{IQR} = Q_3 - Q_1$$ where $Q_1$ and $Q_3$ are the first and third quartiles. 5. **Interpretation:** - The mean score is 80.33, meaning on average, students scored about 80. - The median is 85, indicating half the students scored below 85 and half above. - The mode is 85, showing it was the most common score. - The range is 20, so the scores vary by 20 points from lowest to highest. - The interquartile range is 14, showing the middle 50% of scores are spread over 14 points. This situation helps the teacher understand the overall performance and variability in the class's test results.