Scatter graphs · Year 10

In Year 10 you learn: 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

Other years