Question
Jacquie argued that scatterplots had little value because rarely does a single trend line fit the data. How do you respond? Choose the correct answer below. A. Jacquie is incorrect. A scatterplot gives a representation of the five number summary. The center, the spread, and the overall range can be see easily with this plot. B. Jacquie is incorrect. A scatterplot gives a good visual relationship between two variables. It shows if the relationship is close to a linear one, and if there is a positive, negative, or no association. It Jilso may show presence of outliers. C. Jacquie is incorrect. A scatterplot shows the trend of a variable over time. D. Jacquie is correct.
Ask by Haynes West. in the United States
Feb 03,2025
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**Response:**
Jacquie is incorrect. A scatterplot effectively shows the relationship between two variables, indicating if the relationship is linear and whether it's positive, negative, or nonexistent. It also highlights any outliers in the data.
Solution
The correct answer is:
**B. Jacquie is incorrect. A scatterplot gives a good visual relationship between two variables. It shows if the relationship is close to a linear one, and if there is a positive, negative, or no association. It may also show the presence of outliers.**
**Explanation:**
Scatterplots are valuable tools for visualizing the relationship between two quantitative variables. Even if a single trend line doesn't perfectly fit the data, scatterplots can reveal the nature of the association (positive, negative, or none), the strength of the relationship, and any anomalies or outliers in the data. These insights are crucial for understanding data patterns and informing further analysis, making scatterplots far from valueless.
**Why the other options are incorrect:**
- **A:** Scatterplots are not typically used to represent the five-number summary (minimum, first quartile, median, third quartile, maximum). That summary is more relevant to boxplots or similar visualizations.
- **C:** While scatterplots can include time as one of the variables, they are not specifically designed to show trends of a single variable over time. Time series plots or line charts are more appropriate for that purpose.
- **D:** Since option B provides a better counter-argument to Jacquie's assertion, option D is incorrect.
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The Deep Dive
B. Jacquie is incorrect. A scatterplot gives a good visual relationship between two variables. It shows if the relationship is close to a linear one, and if there is a positive, negative, or no association. It also may show the presence of outliers. Scatterplots are more than just a simple trend line; they allow us to see patterns and correlations between variables at a glance. This visual tool is often used in statistics to identify relationships and potential predictive trends, making it invaluable for data analysis.