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GCSE/Mathematics/WJEC

S6Interpret scatter graphs; correlation and causation

Notes

Scatter graphs, correlation and causation

WJEC examines scatter graphs every Unit 2 paper at Foundation and Intermediate. Higher candidates also need the line-of-best-fit prediction skill.

What is a scatter graph?

A plot of paired (x, y) data points — one axis per variable. Used to investigate whether two variables are related.

Types of correlation

CorrelationMeaningVisual cue
Strong positivey rises as x rises; points cluster tightlyTight band sloping up
Weak positiveupward trend but looseLoose upward scatter
Strong negativey falls as x rises; tightTight band sloping down
Weak negativedownward trend but looseLoose downward scatter
No correlationno clear patternRandom scatter

WJEC standard wording always wants TWO descriptors — the strength (strong/weak) AND the direction (positive/negative).

Line of best fit

A straight line drawn so that points are roughly evenly distributed above and below. By eye, not regression. Three rules:

  1. Don't force the line through the origin.
  2. Don't connect first and last points.
  3. Aim for roughly equal numbers of points either side.

Use the line of best fit to predict y from a given x — read horizontally to the line, then vertically down to the x-axis (or vice versa).

Interpolation vs extrapolation

  • Interpolation — predicting WITHIN the data range. Generally reliable.
  • Extrapolation — predicting OUTSIDE the data range. Unreliable; the relationship may not continue. WJEC awards a B1 for stating "this is extrapolation, so the prediction is unreliable".

Correlation does NOT imply causation

A correlation between ice cream sales and drowning rates exists — both rise in summer. Hot weather is the lurking variable. WJEC wording: "correlation does not mean one variable causes the other; there may be a third (lurking) factor."

Outliers

A point clearly away from the trend. Should usually be ignored when drawing the line of best fit. State "the outlier (x, y) was ignored because it lies far from the trend".

WJEC exam tip

When asked to describe correlation, always use BOTH a strength word and a direction word ("strong positive", "weak negative"). One word alone loses the A1.

AI-generated · claude-opus-4-7 · v3-wjec-maths-leaves

Practice questions

Try each before peeking at the worked solution.

  1. Question 13 marks

    Identify correlation type

    WJEC Unit 2 (Calculator) — Foundation

    Match each scatter graph description to the correlation:

    1. Hours of revision and exam mark.
    2. Daily rainfall in Cardiff and number of beach visitors.
    3. Shoe size and IQ score.

    Choose from: strong positive / strong negative / no correlation. (3 marks)

    Ask AI about this

    AI-generated · claude-opus-4-7 · v3-wjec-maths-leaves

  2. Question 24 marks

    Use line of best fit, identify extrapolation

    WJEC Unit 2 (Calculator) — Intermediate

    A scatter graph plots hours studied (x) against test score (y) for 12 students. Hours range from 0 to 8. A line of best fit is drawn. Using the line, when x = 5 the value of y is 64; when x = 12 the value of y is 110.

    (a) State the type and strength of correlation suggested. (1 mark)
    (b) Estimate the test score for a student who studied 5 hours. (1 mark)
    (c) The line predicts a score of 110 for 12 hours of study. Comment on the reliability of this prediction. (2 marks)

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    AI-generated · claude-opus-4-7 · v3-wjec-maths-leaves

  3. Question 34 marks

    Correlation vs causation

    WJEC Unit 2 (Calculator) — Higher

    A study finds a strong positive correlation between the number of mobile phones owned and life expectancy in 50 countries.

    (a) Describe what "strong positive correlation" means in context. (1 mark)
    (b) A newspaper claims that owning more mobile phones causes people to live longer. Explain whether this conclusion is justified. (3 marks)

    Ask AI about this

    AI-generated · claude-opus-4-7 · v3-wjec-maths-leaves

Flashcards

S6 — Interpret scatter graphs; correlation and causation

7-card SR deck for WJEC GCSE Mathematics — Leaves Batch 2 topic S6

7 cards · spaced repetition (SM-2)