Statistics · Grade 8
Scatter Plots and Data Relationships
A scatter plot displays paired numerical data. The pattern can help describe whether two variables are related.
Learning time: 20–25 minutes · Level: Developing
Learning goals
- Understand the key terms and formulas.
- Apply the method to worked and new examples.
- Check answers and explain the reasoning.
1. Paired data
Each point represents two measurements from the same item or person, such as hours studied and quiz score. Put one variable on each axis and label units.
2. Correlation
Positive correlation means larger x-values tend to occur with larger y-values. Negative correlation means larger x-values tend to occur with smaller y-values. No clear pattern means little or no correlation.
3. Strength and outliers
A strong correlation has points close to a trend; a weak correlation has points more spread out. An outlier is a point far from the general pattern and should be checked, not automatically removed.
4. Line of best fit
A line of best fit summarises the overall trend. It should pass through the middle of the data with roughly balanced points above and below. Use it for cautious estimates within the data range.
5. Correlation is not causation
Two variables can be associated without one causing the other. A third factor may affect both, or the relationship may be coincidental. Avoid claiming cause from a scatter plot alone.
Read patterns without overclaiming
A scatter plot displays paired numerical data. A positive association means larger x-values tend to occur with larger y-values; a negative association means larger x-values tend to occur with smaller y-values. A weak or absent association has no clear upward or downward pattern. An outlier is a point far from the overall pattern and may affect a line of best fit.
Worked reasoning: Suppose study time and quiz score generally rise together. A line of best fit can be used to estimate a score for a given study time, but it does not guarantee an individual result. If the line is y = 6x + 40, a study time of 2 hours gives an estimated score of 52.
Correlation describes a relationship, not proof that one variable causes the other. Sleep, prior knowledge or other factors may influence both study time and scores.
- Describe direction, strength and unusual points.
- Avoid predictions far outside the data range.
- Do not claim causation from a scatter plot alone.
Worked examples
- As temperature rises, ice-cream sales may rise: a positive association.
- As travel speed rises, journey time for a fixed distance tends to fall: a negative association.
- If points show no upward or downward pattern, there may be no clear correlation.
Independent practice
Attempt each problem before reviewing the worked answer.
- What does positive correlation mean? Answer: Both variables tend to increase together.
- What does negative correlation mean? Answer: One tends to increase as the other decreases.
- What is an outlier? Answer: A point far from the general pattern.
- Why label axes with units? Answer: So values and measurements can be interpreted correctly.
- Can correlation prove causation? Answer: No.
- What is a line of best fit used for? Answer: Summarising a trend and making cautious estimates.
- Should an outlier always be deleted? Answer: No; investigate it first.
- Why avoid predictions far beyond observed data? Answer: The pattern may not continue outside the data range.
Knowledge check
Choose one answer for each question, then check for explanations.
Printable worksheet and answer key
Use the independent-practice questions above as a worksheet. Show each step, include units where appropriate, and check your answers after attempting the full set.
Study reminder
Write down the formula or reasoning used for each answer.