Scatter Graphs Answer Key
📊 Part 1: Reading Scatter Graphs
1. Look at the scatter graph showing the relationship between hours of study and test scores. What type of correlation does it show?
Answer: Positive correlation
Explanation: As the hours of study increase, the test scores also increase. The points generally move upward from left to right.
2. From the graph, estimate the test score for a student who studied for 6 hours.
Answer: Approximately 75-80 marks
Method: Find 6 hours on the x-axis, draw a vertical line up to meet the trend of the data points, then read across to the y-axis.
3. Which student appears to be an outlier on the graph?
Answer: The student who studied for 8 hours but only scored 45 marks
Explanation: This point is far away from the general pattern of the other data points.
📈 Part 2: Types of Correlation
4. Match each scatter graph description to its correlation type:
1. As temperature increases, ice cream sales increase
2. As the price of petrol increases, car sales decrease
3. Shoe size and favourite colour
A. Negative correlation
B. No correlation
C. Positive correlation
5. Circle the correct answer: A negative correlation means:
As one variable increases, the other increases
✓
As one variable increases, the other decreases
There is no relationship between the variables
The graph shows negative numbers
🎯 Part 3: Drawing and Interpreting
6. Draw a line of best fit on the scatter graph showing height (cm) vs arm span (cm):
Instructions: Draw a straight line that passes through or near most of the data points, with roughly equal numbers of points above and below the line.
Note: The line should show the general trend - it doesn't need to pass through every point.
7. Using your line of best fit, predict the arm span of a person who is 150cm tall:
Answer: Approximately 148-152cm
Method: Find 150cm on the height axis, follow up to the line of best fit, then read across to the arm span axis.
📋 Part 4: Real-World Applications
8. A scatter graph shows the relationship between daily temperature (°C) and the number of hot drinks sold at a café. Complete the following:
a) The type of correlation would be: negative correlation
b) On a day when the temperature is 25°C, you would expect hot drink sales to be: low
c) The café owner could use this information to: plan stock levels and predict sales based on weather forecasts
9. Check all statements that are true about scatter graphs:
✓
They show relationships between two variables
✓
Each point represents one piece of data
They always show a perfect straight line
✓
They can help us make predictions
All scatter graphs show positive correlation
10. Explain why correlation does not always mean causation. Give an example:
Answer: Just because two things are related doesn't mean one causes the other. There might be other factors involved.
Example: Ice cream sales and drowning incidents both increase in summer, but ice cream doesn't cause drowning - hot weather is the common factor that affects both.
🔍 Part 5: Problem Solving
11. A sports coach collected data on training hours per week and race times (in minutes) for 10 athletes. The scatter graph shows a negative correlation. Explain what this means for the coach:
Answer: The negative correlation means that as training hours increase, race times decrease (athletes get faster).
For the coach: This suggests that more training leads to better performance, so the coach should encourage consistent training to improve race times.
12. Create your own example of two variables that would show:
a) Positive correlation: Hours of practice vs skill level in music
b) Negative correlation: Amount of rainfall vs number of people at the beach
c) No correlation: Hair colour vs mathematics test scores
