Scatter Diagrams (Copy)
Q1 (Non-Calculator)
A scatter diagram plots students’ revision hours (x-axis) against their exam marks (y-axis).
The points trend upwards.
What type of correlation is shown?
Solution:
As revision hours increase, exam marks increase.
This is positive correlation.
Answer:
Positive correlation
Q2 (Non-Calculator)
In a scatter diagram, as the number of hours spent gaming increases, school grades decrease.
What type of correlation is shown?
Solution:
As x increases, y decreases.
This is negative correlation.
Answer:
Negative correlation
Q3 (Non-Calculator)
A scatter diagram shows no clear pattern between shoe size and intelligence.
What type of correlation is shown?
Solution:
No clear relationship.
This is zero correlation.
Answer:
Zero correlation
Q4 (Non-Calculator)
You are asked to draw a line of best fit for a scatter diagram.
What are the two main rules you must follow?
Solution:
- The line must have a roughly equal number of points on either side.
- The line should extend across the full range of the data.
Answer:
Equal distribution of points and full extension across the data range.
Q5 (Non-Calculator)
In a scatter diagram, a student with 5 hours of revision scores 70 marks.
Using the line of best fit, estimate the score for a student who revised 7 hours.
Solution:
- Find 7 on x-axis.
- Follow vertically to the line of best fit.
- Estimate corresponding y-value.
Suppose the line of best fit rises about 10 marks per hour.
From 5 hours (70 marks) to 7 hours: 2 extra hours = about 20 extra marks.
Estimated score = 70 + 20 = 90 marks.
Answer:
Approximately 90 marks
Q6 (Calculator)
A scatter diagram compares height and shoe size of students.
The points lie closely along a straight line.
Is the correlation strong or weak?
Solution:
Points closely clustered around a line indicate strong correlation.
Answer:
Strong correlation
Q7 (Calculator)
In a scatter diagram, you plot temperature against ice-cream sales and see a positive trend.
Predict what happens to ice-cream sales as temperature increases.
Solution:
Ice-cream sales increase as temperature increases.
Answer:
Sales increase
Q8 (Calculator)
A scatter diagram shows number of hours spent practicing piano vs. number of mistakes made.
The graph trends downward.
Describe the correlation.
Solution:
As practice time increases, mistakes decrease.
This is negative correlation.
Answer:
Negative correlation
Q9 (Calculator)
If the scatter diagram shows strong positive correlation, what can you say about the relationship between the two variables?
Solution:
There is a strong linear relationship: as one variable increases, the other also increases.
Answer:
Strong linear relationship (both increase together)
Q10 (Calculator)
In a scatter diagram of exercise time and weight loss, most points are close to a straight line.
What does drawing a line of best fit help you do?
Solution:
- Summarize the trend.
- Predict unknown values inside (or slightly outside) the data range.
Answer:
Summarize trend and make predictions