EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Scatter graphs
Interpreting and representing data · Lesson 3 of 6
Last Lesson and Before
Answer each one, then check.
1. Last lesson: what is a trend?
The general direction of data over time.
2. Last lesson: what goes on the horizontal axis of a time series?
Time
3. Plot (4, 7): which way first?
4 across, then 7 up.
4. Which is continuous: height or number of pets?
Height
Learning Objectives
1. Plot a scatter graph from two sets of data.
2. Describe the correlation: positive, negative or none.
3. Say whether correlation is strong or weak.
4. Identify outliers.
5. Explain that correlation does not prove that one thing causes another.
What Is a Scatter Graph?
A scatter graph shows two sets of data about the same people or things.
▸ Bivariate data. Two measurements for each item: a student's height AND their shoe size.
▸ One point each. Each item is one point, plotted using its two values as coordinates.
▸ Do not join the points. The points are separate items; there is no order to follow.
▸ Look at the shape. The pattern of the points shows whether the two measurements are related.
Types of Correlation
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Positive correlation means as one value increases, so does the other. Negative correlation means as one increases, the other decreases. No correlation means there is no clear relationship at all. |
Up together, one up and one down, or no pattern at all. |
Describing Correlation
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Positive As one goes up, the other goes up. Height and shoe size. |
Negative As one goes up, the other goes down. The age of a car and its value. |
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No correlation No relationship. Height and score in a maths test. |
Strong or weak Strong: the points lie close to a straight line. Weak: they are more spread out but still show a pattern. |
Outliers
An outlier is a point that does not fit the pattern of the rest.
▸ Spotting one. A point well away from the others - for example, a very old car that is worth a lot because it is a classic.
▸ Why it happens. A mistake in recording the data, or a genuinely unusual item.
▸ What to do. Do not simply delete it. Note it, and think about why it is different.
▸ In the exam. You may be asked to circle it or give its coordinates.
Correlation Is Not Causation
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WHAT CORRELATION SHOWS |
WHAT IT DOES NOT SHOW |
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▸ Two things tend to change together. ▸ It can help you make predictions. ▸ It can suggest an idea worth testing. |
▸ That one thing causes the other. ▸ Ice cream sales and sunburn are positively correlated - but ice cream does not cause sunburn. ▸ Both are caused by a third thing: hot, sunny weather. |
Case Study
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CASE STUDY "Storks Deliver Babies" In 2000 the statistician Robert Matthews published a paper called "Storks Deliver Babies (p = 0.008)". Using data from 17 European countries, he showed a genuine positive correlation between the number of breeding pairs of storks in a country and the number of babies born there each year. Of course storks do not deliver babies. Bigger countries simply have more room for storks AND more people having babies. His point was that a strong correlation, however convincing it looks, never proves that one thing causes the other. |
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2000 Matthews publishes the stork paper |
17 European countries in his data |
Key Terms
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Scatter graph A graph plotting two sets of data about the same items as points. |
Bivariate data Data with two values for each item. |
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Correlation A relationship between two sets of data. |
Positive correlation As one value increases, the other increases. |
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Negative correlation As one value increases, the other decreases. |
Outlier A value that does not fit the pattern of the rest of the data. |
Your Task: Correlated or Not?
10 minutes
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For each pair, predict the correlation (positive, negative or none) and say whether one could cause the other. (a) Temperature outside and number of hot drinks sold. (b) Hours of revision and test score. (c) Arm span and height. (d) House number and number of people living there. (e) Number of firefighters at a fire and the damage done. 1. Predict the correlation. 2. Decide if one causes the other. 3. Look for a hidden third factor. |
A good answer shows: (a) Negative; plausibly causal. (b) Positive; plausibly causal, but other factors matter. (c) Strong positive; both depend on body size. (d) None. (e) Positive - but firefighters do not cause damage: bigger fires need more firefighters AND cause more damage.
Can I...?
☐ Plot a scatter graph.
☐ Describe positive correlation.
☐ Describe negative correlation.
☐ Recognise no correlation.
☐ Say if correlation is strong or weak.
☐ Identify an outlier.
☐ Interpret correlation in context.
☐ Explain that correlation is not causation.
Summary
✓ A scatter graph plots two measurements for each item; do not join the points.
✓ Correlation is positive, negative or none, and strong or weak.
✓ An outlier does not fit the pattern.
✓ Correlation does not prove causation: look for a third factor.
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EXAM FOCUS Describe the relationship between the temperature and the number of hot chocolates sold. (1 mark) "Describe the relationship" wants a sentence in context: "as the temperature increases, the number of hot chocolates sold decreases". Just "negative" may not get the mark. |