Scatter graphs plot pairs of data to show relationships. Correlation describes the strength and direction of the relationship.
Core Concepts
Types of Correlation
- Positive: as one increases, the other increases.
- Negative: as one increases, the other decreases.
- No correlation: no clear pattern.
Strength
- Strong: points close to a line.
- Weak: points spread more widely.
Line of Best Fit
A straight line that best represents the trend. It should:
- Pass through the mean point .
- Have roughly equal numbers of points above and below.
Using the Line of Best Fit
Interpolation: estimating within the data range (reliable). Extrapolation: estimating outside the data range (unreliable).
Outliers
Points far from the general trend. May be errors or unusual cases.
Worked Example: Example
Problem
Plot height vs. shoe size for 10 students. Draw line of best fit. Use it to estimate shoe size for a student of height 170 cm.
Solution
Practice Problems
- Describe the correlation: temperature vs. ice cream sales.
- Why is extrapolation unreliable?
- Identify the outlier from a scatter graph.
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Key Takeaways
Positive, negative, or no correlation.
Line of best fit through the mean point.
Interpolation is reliable; extrapolation is not.
Correlation ≠ causation.