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3.7 Scatter Graphs

GCSE Maths Foundation · Edexcel · Chapter 3: Graphs, tables and charts

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: plotting scatter graphs, describing correlation, outliers and causation. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

  • Plot a scatter graph from paired data
  • Describe correlation as positive, negative or none, and as strong or weak
  • Explain what the correlation means in context
  • Spot an outlier and know that correlation does not prove one thing causes another

Key words

  • Scatter graph: A graph of pairs of values plotted as points (crosses), used to look for a relationship.
  • Correlation: A relationship between two variables shown by the pattern of the points.
  • Positive correlation: As one variable increases, the other tends to increase.
  • Negative correlation: As one variable increases, the other tends to decrease.
  • Outlier: A point that does not fit the general pattern of the data.
  • Causation: When a change in one variable actually causes the change in the other.

Plotting a scatter graph

Each pair of values gives one point. Put one variable on each axis, use an even scale, and plot each point with a small cross. Do not join the points.

  • Test score; 1 32; 2 41; 3 45; 4 52; 5 58; 6 63; 7 71; 8 74

Worked example: plotting a point

The student who revised for 5 hours scored 58.
Go along to 5 on the horizontal axis, then up to 58 (just under 60), and draw a cross.

Answer: the point (5, 58)

Types of correlation

Look at the overall pattern of the crosses.

  • Positive: the points go up from left to right.
  • Negative: the points go down from left to right.
  • No correlation: the points are scattered with no pattern.

Worked example: describing in context

Describe the relationship shown by the revision graph.
The points go up from left to right, close to a straight line.

Answer: strong positive correlation: the more hours students revised, the higher their test scores tended to be

Strong and weak correlation

If the points lie close to a straight line the correlation is strong. If they are more spread out but still show a trend, it is weak.

Worked example: what would you expect?

Age of a car and its value: older cars are usually worth less, so negative correlation.
Height and arm span: taller people usually have longer arm spans, so strong positive correlation.
Shoe size and maths test score: no link, so no correlation.

Answer: negative, positive, none

Outliers and causation

An outlier is a point that is well away from the pattern. It may be a mistake or an unusual case. Correlation shows that two things are linked; it does not prove that one causes the other.

Worked example: correlation is not causation

In a town, sales of fans and sales of ice lollies show strong positive correlation.
Buying fans does not make people buy ice lollies. Both go up in hot weather.

Answer: the link is caused by a third factor: the temperature

Common mistakes

  • Joining the points with lines like a line graph.
  • Only writing "positive" without explaining what it means in context.
  • Calling weak correlation "no correlation". If there is a trend, say it is weak.
  • Saying one variable causes the other just because they are correlated.

Revision questions

Try these, then check your answers below each one.

Question 1. What type of correlation would you expect between a person's height and their arm span? (Choose from: Positive, Negative, No correlation.)

Answer: Positive

Working: Taller people tend to have longer arm spans: positive correlation.

Question 2. What type of correlation would you expect between the outside temperature and the number of coats sold? (Choose from: Positive, Negative, No correlation.)

Answer: Negative

Working: As the temperature goes up, fewer coats are sold: negative correlation.

Question 3. What type of correlation would you expect between shoe size and the last digit of a person's phone number? (Choose from: Positive, Negative, No correlation.)

Answer: No correlation

Working: There is no link, so no correlation.

Related lessons

Continue in the full course

This lesson is section 3.7 (EGCMF0307) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.

 

 

 

 

 

 

 

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