AP Statistics 2.4 Representing the Relationship Between Two Quantitative Variables Study Notes
AP Statistics 2.4 Representing the Relationship Between Two Quantitative Variables Study Notes- New syllabus
AP Statistics 2.4 Representing the Relationship Between Two Quantitative Variables Study Notes -As per latest AP Statistics Syllabus.
LEARNING OBJECTIVE
- Graphical representations and statistics allow us to identify and represent key features of data.
Key Concepts:
- Representing Bivariate Quantitative Data with Scatterplots
Representing Bivariate Quantitative Data with Scatterplots
Representing Bivariate Quantitative Data with Scatterplots
A scatterplot is a graph that represents two quantitative variables measured on the same individuals. Each individual is shown as a point with coordinates \((x, y)\), where:
- The horizontal axis (x-axis) represents the explanatory variable (independent variable).
- The vertical axis (y-axis) represents the response variable (dependent variable).
Purpose: Scatterplots are used to visually identify patterns, trends, clusters, or unusual observations in the relationship between two quantitative variables.
Characteristics of a Scatterplot
When describing a scatterplot, focus on the following features:
Direction: The overall trend of the data.
- Positive association: As \(x\) increases, \(y\) tends to increase.
- Negative association: As \(x\) increases, \(y\) tends to decrease.
- No association: No clear pattern is visible.
Form: The shape of the relationship.
- Linear (points follow a straight-line pattern).
- Nonlinear (curved relationship).
Strength: How closely the points follow a clear form.
- Strong: Points are close to the line/curve.
- Weak: Points are widely scattered.
Outliers: Individual points that fall outside the general pattern.
Example
A researcher records the number of hours studied (x) and the exam scores (y) of 20 students. A scatterplot shows that as hours studied increase, exam scores generally increase, with points lying close to a straight line.
How would you describe the scatterplot?
▶️ Answer / Explanation
Direction: Positive (more hours studied → higher scores).
Form: Linear pattern.
Strength: Strong (points close to the line).
Outliers: One student studied for 10 hours but scored very low, which does not fit the overall pattern.
Conclusion: The scatterplot shows a strong, positive, linear association between hours studied and exam scores.
Example
A health researcher measures shoe size (x) and math test score (y) for a group of 50 students. The scatterplot shows points scattered randomly with no clear upward or downward trend.
How would you describe the scatterplot?
▶️ Answer / Explanation
Direction: None (as shoe size increases, math score does not systematically change).
Form: No clear form (neither linear nor curved).
Strength: Very weak — points are widely scattered.
Outliers: A few extreme shoe sizes, but they do not affect the lack of relationship.
Conclusion: The scatterplot shows no association between shoe size and math score. The variables are unrelated.