Scatter Graphs
Does more revision lead to higher grades? Does warmer weather mean more ice creams sold? Scatter graphs let you explore relationships between two sets of data at a glance — and they’re used everywhere from sports analytics to business planning.
Types of Correlation
Correlation describes how two variables change together. We judge both the type (positive, negative, or none) and the strength (strong or weak, based on how close the points are to a straight line).
Positive Correlation
As one variable increases, the other also tends to increase. Points run upward from left to right.
Example: Hours revising vs. exam score.
Negative Correlation
As one variable increases, the other tends to decrease. Points run downward from left to right.
Example: Temperature vs. hot drinks sold.
No Correlation
No clear pattern — the points are scattered randomly and the variables don’t appear to be related.
Example: Shoe size vs. intelligence.
Key Ideas
The Line of Best Fit
When there is correlation, draw a straight line that shows the general trend — roughly the same number of points above and below it. Use it to make predictions:
- Interpolation: Predicting within the data range — reliable.
- Extrapolation: Predicting outside the data range — unreliable, as the trend may not continue.
Correlation ≠ Causation
Just because two things are correlated does not mean one causes the other. A hidden third factor could be responsible.
Classic example: Ice cream sales and drownings are positively correlated — but ice cream doesn’t cause drownings. Hot weather causes both to increase independently.
Worked Example: Temperature vs. Hot Drinks Sold
| Temperature (°C) | Hot Drinks Sold |
|---|---|
| 5 | 70 |
| 10 | 55 |
| 12 | 50 |
| 15 | 40 |
| 18 | 35 |
| 20 | 25 |
| 22 | 20 |
Interpretation: The points show a clear downward trend — this is a strong negative correlation. As temperature increases, hot drinks sold decreases.
- Interpolation (reliable): From the line of best fit at 14°C → approximately 42–45 hot drinks.
- Extrapolation (unreliable): Extending the line to 25°C → approximately 10–15 drinks. Unreliable because it’s outside the data range.
Tutor Insights
🤔 Common Misunderstandings
- The line must pass through the origin or specific points. It doesn’t — it’s about the overall trend.
- Confusing “strong” and “weak” correlation. Strong = points close to a straight line. Weak = spread out but with a general trend.
- Assuming correlation means causation. It never does on its own.
- Mixing correlation with relationship. “Positive correlation” is the mathematical term; “as X increases, Y increases” describes the relationship in context.
📝 Common Exam Mistakes
- Poor plotting or missing axis labels and titles.
- A curved or unbalanced line of best fit — it must be straight, with roughly equal points above and below.
- Describing correlation as “upwards” rather than “positive”.
- Forgetting to comment on reliability when making an extrapolation prediction.
Practice Questions
- A student recorded hours spent playing video games versus their Maths test score:
(a) Plot a scatter graph for this data.
Hours Playing Games Maths Score (%) 2 75 5 60 7 50 3 70 8 45 1 80 6 55 4 65
(b) Describe the type and strength of correlation. - For each of these descriptions, state the type of correlation and sketch the scatter graph:
(a) As a car gets older, its value decreases.
(b) The number of pets someone owns vs. their shoe size.
(c) A person’s height vs. their arm span. - A scatter graph shows hours of sunshine vs. ice cream sales, with a clear positive correlation and an outlier at (1, 30).
(a) Describe the correlation.
(b) Describe the relationship in context.
(c) Explain why (1, 30) might be an outlier.
(d) Estimate sales for 5.5 hours of sunshine using a line of best fit and comment on reliability.
(e) Estimate sales for 12 hours and comment on reliability. - A student finds a positive correlation between the number of teachers in a school and exam results. Explain why this doesn’t prove that more teachers cause better results.
- Explain the difference between “strong positive correlation” and “weak positive correlation”.
Show Answers
- (a) Plot with Hours (0–8) on x-axis, Score (40–80) on y-axis. (b) Strong negative correlation — as hours playing games increases, Maths scores decrease. Points cluster closely around a downward trend.
- (a) Negative — as age increases, value decreases. (b) No correlation — shoe size and number of pets are unrelated. (c) Positive — taller people tend to have longer arm spans.
- (a) Strong positive correlation. (b) As sunshine hours increase, ice cream sales generally increase. (c) At 1 hour of sunshine, sales of 30 is much higher than the trend would suggest — perhaps a special event or local factor caused unusually high sales. (d) Around 23–26 ice creams — this is interpolation and is reliable. (e) Around 42–45 — this is extrapolation and is unreliable as the trend may not continue outside the data range.
- Correlation does not prove causation. Schools with more teachers may also have more funding, smaller class sizes, or better resources — these other factors are more likely to explain better results. A third variable could account for both.
- Strong positive: Points are very close to a straight upward line — a very consistent relationship. Weak positive: Points are more spread out but still show a general upward trend — a less consistent relationship.
FAQs
Q: What is the difference between strong and weak correlation?
A: Strong correlation means the points are very close to a straight line. Weak correlation means the points are more spread out but still show a general trend in one direction.
Q: Do I always have to draw a line of best fit?
A: Only if there is a clear positive or negative correlation and you are asked to make predictions. You would not draw one for “no correlation”.
Q: Why can’t I assume causation from correlation?
A: Correlation shows that two things tend to change together. A hidden third factor could be influencing both, or the relationship could be coincidence. Always look for alternative explanations.
Q: Can a scatter graph show more than two variables?
A: No — a standard scatter graph shows exactly two variables, one on each axis. It is specifically designed to explore the relationship between a pair of variables.
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