Answer Keys: Scatter Plots and Data Analysis

Student Concept Worksheet Answers

1

Negative association

As temperature increases, hot chocolate sales decrease. When one goes up and the other goes down, it's negative.

2

No association

There's no logical relationship between shoe size and test scores - knowing someone's shoe size tells you nothing about their test score.

3

Non-linear

People don't grow at a constant rate. They have growth spurts during puberty, then growth levels off. The pattern would be curved, not straight.

4

70

Since 4 is exactly halfway between 2 and 6, the y-value should be halfway between 50 and 90. (50 + 90) / 2 = 70

Practice Worksheet Answers

Part A: Identify the Association

#	Answer	Explanation
1	Negative	Price up, sales down = negative association
2	Negative	More practice, fewer mistakes = negative association
3	Positive	Higher temp, more beach-goers = positive association
4	No association	Height and favorite color are unrelated

Part B: Describe in Context

5

Sample: "As study time increases, test scores tend to increase."

Accept any response that correctly states both variables and describes the positive relationship.

6

Sample: "As the age of a car increases, its resale value tends to decrease."

Accept any response that correctly states both variables and describes the negative relationship.

Part C: Linear or Non-Linear

#	Answer	Explanation
7	Non-linear	Ball goes up then comes down - parabolic shape
8	Linear	Constant price per item means constant rate of change
9	Non-linear	Exponential growth (1, 2, 4, 8...) is curved
10	Linear	Constant speed means constant rate of change

Part D: Analyze Data

11

Negative association

As TV hours increase, exercise hours decrease

12

Sample: "As the number of hours watching TV increases, the number of hours spent exercising tends to decrease."

13

Positive linear association

As study time increases, quiz scores increase at a fairly constant rate

14

About 99-100

The pattern shows approximately 6-8 points gained per half hour. Following the pattern: 94 + 6 = 100 (or close to it)

Part E: Line of Best Fit

15

45

Slope = (60-30)/(8-2) = 30/6 = 5. At x=2, y=30. At x=5: y = 30 + 5(3) = 45. Or: x=5 is halfway, so y = (30+60)/2 = 45

16

38

y = 4(7) + 10 = 28 + 10 = 38

Challenge Questions:

#17: No, ice cream doesn't cause drowning! Both are affected by a third variable: warm weather/summer. In summer, more people eat ice cream AND more people swim, which leads to more drowning incidents. This is called a confounding variable - correlation does not prove causation!

#18: Student B's line is better. A good line of best fit should have approximately equal points above and below it, showing the overall trend. It doesn't need to pass through the data points - it should represent the "average" direction of all the points.

FAST Practice Quiz Answers

1

B) Negative linear association

As exercise increases, heart rate decreases - this is a negative relationship.

2

B) Negative association; as temperature increases, hot drink sales decrease

Temperature goes up (30 to 80), sales go down (85 to 18) - negative association.

3

B) 45

From (2, 25) to (10, 65): slope = (65-25)/(10-2) = 40/8 = 5. At x=6: y = 25 + 5(4) = 45. Or: x=6 is halfway between 2 and 10, so y = (25+65)/2 = 45.

4

Select: A, D, E

A) Positive = both increase together - TRUE
B) Line must pass through every point - FALSE (shows trend, not individual points)
C) Association proves causation - FALSE (correlation ≠ causation)
D) Negative = one up, one down - TRUE
E) Equal points above and below - TRUE

5

B) As cars get older, their fuel efficiency tends to decrease

Negative association means as age increases, fuel efficiency decreases. Note: The word "tends" is important - it's not always true for every car, just the general trend.

6

B) For every additional hour worked, earnings increase by $3

The slope (3) represents the rate of change - the amount y changes for each 1-unit change in x. In context: $3 earned per hour worked.

FAST Quiz Scoring Guide

Score	Interpretation	Recommended Action
6/6	Mastery	Ready for more complex data analysis and regression concepts.
4-5/6	Approaching Mastery	Review specific concepts missed (predictions, interpreting slope, etc.).
2-3/6	Developing	Reteach association types with clear visual examples. Focus on vocabulary.
0-1/6	Needs Intervention	Small group instruction. Start with basic graphing and identifying simple patterns.

Common Error Analysis:

Confusing positive/negative: If Q1 or Q2 were wrong, review that positive = both increase, negative = one increases while other decreases.
Prediction errors: If Q3 was wrong, practice finding slope and using it to interpolate values.
Causation misconception: If Q4 included option C, emphasize that association (correlation) does NOT prove causation.
Interpretation errors: If Q5 or Q6 were wrong, practice translating mathematical concepts into real-world context.