https://file.aiquickdraw.com/mathbot/file/1730421530229f8dr64zy.jpg

Let's analyze the question part (a) and the table provided.

### Question (a) Analysis
We need to explain why 2020 stands out compared to the other years (2017, 2021, and 2023) in terms of mean and standard deviation.

### Observations from the Table
1. **Mean Turbidity**:
   - 2020 has the highest mean turbidity at **2.73**, which is significantly higher than the other years:
     - 2017: 1.42
     - 2021: 1.24
     - 2023: 1.17
   - This indicates that the overall turbidity in 2020 was much greater on average compared to the other years, suggesting worse water clarity.

2. **Standard Deviation**:
   - 2020 also has the highest standard deviation, **0.91**, compared to:
     - 2017: 0.42
     - 2021: 0.64
     - 2023: 0.40
   - A higher standard deviation means there was more variability in the turbidity measurements in 2020, showing that the turbidity levels fluctuated more widely compared to the other years. This could indicate more frequent or extreme changes in water quality within that year.

### Explanation
Combining these observations:
- The high mean in 2020 suggests overall worse water clarity during that year.
- The high standard deviation in 2020 indicates inconsistent turbidity levels, meaning that conditions likely fluctuated more drastically than in the other years. This variability could point to environmental factors or events in 2020 that disrupted water clarity more than in other years.

Would you like further details on standard deviation's role, or have any other questions?

### Additional Related Questions
1. What could cause higher variability in turbidity levels, as seen in 2020?
2. How might environmental factors like weather influence annual turbidity data?
3. Why is a high standard deviation often a sign of extreme conditions or outliers?
4. How does turbidity impact aquatic ecosystems?
5. Could higher turbidity affect human activities, like recreation or water treatment?

### Tip
When analyzing data, always consider both the mean and standard deviation, as together they provide insights into both the central tendency and the variability of the data set.

2020 is clearly worse than the other three years. Explain why, using both the mean and the standard deviation.

Explore why 2020 had worse turbidity data compared to other years by analyzing the mean and standard deviation. This statistical problem involves understanding the central tendency and variability of data, making it suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation