Learn to reason about and solve Grade 8 problems involving Scatter Plots and Patterns in Data.
The scatter plot below shows age (in years) on the \(x\)-axis and income (in thousands of dollars) on the \(y\)-axis for 10 employees. Describe the correlation between age and income.
A scatter plot shows the relationship between ice cream sales and drowning incidents across summer months. Both variables increase together, yielding \(r = 0.89\). A researcher concludes that ice cream sales cause drowning deaths. Is this conclusion valid?
A scatter plot displays student GPA versus hours watched TV per week. Most students show a pattern: those who watch more TV have lower GPAs. A student with a GPA of 3.8 watches 15 hours of TV per week, while similar high watchers have GPAs around 1.4–2.0. Is this student an outlier?
A scatter plot of advertising budget (thousands of dollars) versus sales revenue (thousands) displays a curved, accelerating upward pattern. Initially, each dollar spent increases sales by 10 dollars; later, each dollar spent increases sales by 25 dollars. Which term describes this relationship?
A researcher plots the relationship between student test anxiety and exam performance for 50 students. The scatter plot shows points forming a clear cluster: anxious students (high anxiety scores) cluster at lower exam scores, while calm students (low anxiety) cluster at higher exam scores. What is the shape of this cluster pattern?
Two scatter plots compare the same dataset. Plot A omits one extreme outlier; Plot B includes it. How do you expect the correlation coefficient to change when the outlier is added?
A scatter plot shows plant growth (cm) versus amount of water given (liters) over 8 weeks. The first 3 liters produce rapid growth; beyond 3 liters, additional water causes little additional growth, then declining growth past 5 liters (from overwatering). This pattern is best described as:
A scatter plot compares weekly training time and sprint time for two groups. Red points represent recreational students, and blue points represent competitive sprinters. Which statement best describes the graph?
The points form an upward trend. As age increases, income increases, showing a positive correlation. Perfect would mean all points lie exactly on a line.
High correlation between ice cream and drowning likely reflects a common cause: warm weather increases both ice cream sales and swimming activity. Correlation alone cannot prove that one variable causes changes in another.
Most students show: more TV → lower GPA. This student breaks that pattern with high TV but also high GPA, making this point an outlier that deviates from the trend.
The changing return on spending (10 dollars → 25 dollars) indicates a nonlinear relationship. A linear relationship would show constant returns.
The points form a diagonal band from upper left (low anxiety, high score) to lower right (high anxiety, low score), displaying negative correlation with clustered variation.
In this plot, the outlier sits far from the upward trend line, so it increases scatter and weakens the correlation coefficient.
The relationship changes from steeply increasing to flat to decreasing. This curve (inverted parabola) is nonlinear—the rate of change is not constant and the direction reverses.
The red points form one cluster, and the blue points form another. The graph therefore contains two distinct groups rather than one random set or one common linear pattern.
