Grade 8 Mathematics
A SCATTER PLOT shows the relationship between TWO variables.
We look for patterns called ASSOCIATIONS - does one variable change as the other changes?
A LINE OF BEST FIT helps us see the trend and make predictions!
As x increases, y INCREASES
Goes UP from left to right
As x increases, y DECREASES
Goes DOWN from left to right
No clear pattern
Points are scattered randomly
A researcher collected data on hours of sleep and number of mistakes made on a test:
| Hours of Sleep | Mistakes |
|---|---|
| 4 | 12 |
| 5 | 10 |
| 6 | 8 |
| 7 | 5 |
| 8 | 3 |
| 9 | 2 |
Identify variables: x = hours of sleep, y = number of mistakes
Look at the pattern: As sleep increases (4, 5, 6, 7, 8, 9), mistakes decrease (12, 10, 8, 5, 3, 2)
Identify association: NEGATIVE association (one goes up, the other goes down)
Interpret in context: "As the number of hours of sleep increases, the number of mistakes tends to decrease."
The scatter plot shows hours studied vs. test scores.
Points: (1, 65), (2, 70), (3, 72), (4, 80), (5, 85), (6, 88)
Look at the pattern: Points go UP from left to right = POSITIVE linear association
Draw the line: The line should follow the direction of points with roughly equal points above and below
Make a prediction: Using the line, if a student studies 7 hours, we can predict they might score around 92-95.
WRONG: "The scatter plot shows that sleeping more CAUSES fewer mistakes." We can't prove causation from a scatter plot!
RIGHT: "The scatter plot shows that more sleep is ASSOCIATED WITH fewer mistakes." Association means there's a relationship, but we can't prove one CAUSES the other.
1. A scatter plot shows the relationship between temperature (x) and hot chocolate sales (y). As temperature increases, sales decrease. What type of association is this?
Association type:
2. A scatter plot shows the relationship between shoe size and test scores. The points are scattered with no pattern. What type of association is this?
Association type:
3. The scatter plot below shows age (x) and height (y) for students ages 5-18. Is this association linear or non-linear? Explain.
Hint: Do people grow at a constant rate, or do they have growth spurts?
Linear or Non-linear:
Explanation:
4. A line of best fit passes through (2, 50) and (6, 90). Use these points to predict the y-value when x = 4.
Hint: 4 is exactly halfway between 2 and 6!
Predicted y-value: