Scatter graphs · Grade 8
In Grade 8 you learn: scatter plots, correlation, and lines of best fit.
A scatter graph plots pairs of measurements, such as temperature and drinks sold, as points. The pattern shows whether the two are related (correlated), and a line of best fit lets you estimate one value from the other.
Key facts
- Positive correlation: as one variable increases, the other tends to increase.
- Negative correlation: as one variable increases, the other tends to decrease.
- No correlation: no clear pattern.
- A line of best fit follows the trend, with about as many points above it as below. It need not go through (0, 0).
- Interpolation (inside the range of the data) is fairly reliable. Extrapolation (outside it) is not.
- An outlier is a point that does not fit the pattern.
- Correlation does not prove that one thing causes the other.
Worked examples
Example 1
Describe the correlation between temperature and hot drinks sold.
Answer: Strong negative correlation
Example 2
The line of best fit for revision and test score is y = 5x + 20. Estimate the score of a student who revised for 6 hours.
Answer: 50
Example 3
A line of best fit passes through (2, 30) and (8, 60). The data cover 1 to 9 hours of revision. Find the gradient and say why a prediction for 20 hours is unreliable.
Answer: 5 marks per hour; 20 hours is far outside the data