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Scatter diagrams

Plotting paired data, spotting correlation, and drawing a line of best fit.

  • Define and explain Scatter diagrams in your own words
  • Use key terms such as Correlation accurately
  • Apply what you have learned to new examples and questions
  • Avoid the common mistakes learners make with this topic

This lesson focuses on Scatter diagrams: plotting paired data, spotting correlation, and drawing a line of best fit.

Definition: Scatter diagrams

Plotting paired data, spotting correlation, and drawing a line of best fit.

Key ideas

Correlation is not causation

A strong correlation only shows that two things vary together; a third factor may cause both. A line of best fit drawn through the middle of the points shows the trend and can estimate values within the data range, but never extrapolate far beyond it.

Reading charts carefully

Check the axes first: a bar chart that starts above zero can exaggerate small differences, and a pie chart must show sectors proportional to the data. Frequency diagrams need equal class widths, or frequencies must be scaled by width.

Key term — Correlation: A pattern in a scatter diagram where two variables move together — positive, negative or none — which does not by itself prove causation.

Worked example: Scatter diagrams

A scatter diagram shows points rising left to right. What type of correlation is this?

Positive correlation.

Answer: Positive correlation.

Common mistakes
  • Finding the median without ordering the data Always sort the values first; the median is the middle of the ordered list, not the middle of the original list.
  • Forgetting that an even count has no single middle value With an even number of values, the median is halfway between the two middle values, e.g. (6 + 8) ÷ 2 = 7.

Practice

Six test scores are 5, 6, 7, 8, 9 and 40. Which average best represents a typical score?
One value is extreme.

The median (7.5); the mean (12.5) is distorted by the outlier 40.

Find the mean of 4, 7, 9, 12, 18.
Add, then divide by 5.

Sum = 50; mean = 50 ÷ 5 = 10.

Find the median of 11, 4, 9, 2, 7.
Order the data first.

Ordered: 2, 4, 7, 9, 11; median = 7.

Find the mode and range of 2, 6, 4, 6, 6, 3.
Mode is most frequent; range is max minus min.

Mode = 6; range = 6 − 2 = 4.

Quick check

Scatter diagrams — quick check

Which of these best defines "Correlation"?

A pattern in a scatter diagram where two variables move together — positive, negative or none — which does not by itself prove causation.

Why might a bar chart with a y-axis starting at 50 be misleading?

Bars look far more different than the values are, because the truncated axis exaggerates small differences.
Key takeaways
  • Scatter diagrams: plotting paired data, spotting correlation, and drawing a line of best fit.
  • Correlation is not causation: A strong correlation only shows that two things vary together; a third factor may cause both.
  • Median: The middle value when data is ordered from smallest to largest; a robust average unaffected by extreme values.
  • Watch out for: finding the median without ordering the data
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