Scattergraphs
Probability and statistics
- Foundation
- Non-calculator
- 8 questions
- 29 marks
These are original practice questions, not a past paper. This site is independent and not affiliated with AQA or Pearson.
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The graph plots hours of revision against test score. What type of correlation does it show, ignoring the outlier?
Revision hours and test score. The square point is separate from the pattern. 2 marks
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Describe the relationship shown by the points that follow the pattern.
2 marks
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Write the coordinates of the outlier.
3 marks
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A sensible line of best fit is close to $y = x + 1.5$, where $x$ is hours and $y$ is the score. Use a line of best fit to estimate the score for $5$ hours of revision.
3 marks
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Explain why an estimate at $5$ hours is more reliable than an estimate at $12$ hours.
4 marks
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A student says the graph proves that extra revision causes a higher score. Comment on that claim.
4 marks
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Match the likely correlation: ice-cream sales and temperature; rainfall and sunglasses sales; shoe size and maths score.
5 marks
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Use the graph to estimate the score for $3.5$ hours of revision. Explain the effect of adding the point $(6, 2)$, and why the line should not be used to predict a score for $20$ hours.
6 marks
Mark scheme
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Answer. Positive correlation
- As the hours increase, the scores generally increase.
- Positive correlation
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Answer. Students who revised for more hours tended to get higher scores.
- The relationship is positive.
- More revision is associated with a higher score.
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Answer. $(8, 2)$
- The square point does not follow the upward pattern.
- $(8, 2)$
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Answer. About $6.5$. Accept $6$ to $7$ if it follows the line.
- The estimate should follow the main pattern, not the outlier.
- Around $6.5$ is consistent with the line through the main points.
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Answer. Five hours is inside the data. Twelve hours is beyond it, so that estimate is extrapolation.
- Interpolation is inside the range of the plotted hours.
- The pattern may not continue as far as $12$ hours.
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Answer. The graph shows an association, not proof of cause. Another factor could affect both revision and score.
- Correlation is not the same as causation.
- The outlier also shows that a high number of hours does not guarantee a high score.
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Answer. Positive; negative; none
- Warmer weather is associated with more ice-cream sales.
- More rain is associated with fewer sunglasses sales.
- Shoe size and maths score have no expected linear relationship.
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Answer. About $5$, accept $4.5$ to $5.5$. The new point would weaken the correlation. Twenty hours is far outside the data.
- Read the estimate from a line that follows the main cluster.
- $(6, 2)$ is well below the pattern, so the correlation becomes weaker.
- Predicting at $20$ hours is extrapolation, a long way beyond the plotted values.