Show — 3 marks
A student investigates the relationship between the thickness of insulation material (in cm) and the time taken for hot water to cool from 70°C to 20°C (in minutes). The student wraps identical containers of hot water in different thicknesses of insulation and measures the cooling time. The results are plotted on a scatter graph.
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(a) The student obtains the following data:
Insulation thickness (cm): 1, 2, 3, 4, 5, 6
Cooling time (minutes): 8, 15, 22, 28, 36, 41
Show that there is a positive correlation between insulation thickness and cooling time.
[1 mark]
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(b) Describe the strength of this correlation and explain what this tells us about the relationship between the variables.
[1 mark]
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(c) The student claims that 'increasing insulation thickness causes water to cool more slowly'. Using your knowledge of correlation and causation, show why this conclusion may not be valid based solely on the scatter graph data.
[1 mark]
Show mark scheme
- (a) As insulation thickness increases, cooling time increases / the points show an upward trend from left to right / as x increases, y increases
- (b) Strong/very strong positive correlation; the points lie close to/approximately on a straight line / there is very little scatter around the trend
- (c) Correlation does not prove causation / other variables may affect cooling time (e.g. room temperature, container material, initial water temperature) / a third variable could cause both insulation thickness and cooling time to increase / the scatter graph alone cannot establish a causal relationship
Define — 5 marks
A physics student investigates the relationship between the mass of a falling object and the time it takes to fall from a fixed height in air. She collects data from 12 different objects and plots a scatter graph with mass on the x-axis and time on the y-axis. The plotted points show very little pattern or trend.
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(a) Define what is meant by correlation in the context of a scatter graph.
[2 marks]
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(b) The student's results show no correlation between mass and time. Explain what this means for the relationship between these two variables.
[2 marks]
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(c) Define the term 'anomalous result' and identify why one of the student's data points might be anomalous if it lay far away from the general scatter of points.
[1 mark]
Show mark scheme
- (a) Correlation describes the relationship / connection / association between two variables shown on a scatter graph (1 mark)
- (a) It indicates how closely the data points follow a pattern or trend (1 mark)
- (b) No correlation means there is no clear relationship / pattern / trend between mass and time (1 mark)
- (b) Changes in mass do not affect / are not linked to changes in time taken to fall / the two variables are independent (1 mark)
- (c) An anomalous result is a data point that does not fit the general pattern / lies far from the trend / is significantly different from other results, possibly due to experimental error or unusual conditions (1 mark)
State — 4 marks
A student investigates the relationship between the thickness of insulation material (in cm) and the rate of heat loss (in W) from a hot water tank. The student collects data from 12 different tanks with varying insulation thicknesses and plots the results on a scatter graph. The graph shows points that follow a clear downward trend from left to right, with most points lying close to an imaginary straight line, though three points deviate noticeably from this pattern.
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(a) State the type of correlation shown by the scatter graph.
[1 mark]
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(b) State the strength of the correlation shown by the scatter graph, and justify your answer with reference to the distribution of points.
[2 marks]
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(c) State what the three points that deviate from the main trend suggest about the reliability of using this scatter graph to make predictions about heat loss from insulation thickness. Explain your reasoning.
[1 mark]
Show mark scheme
- (a) Negative correlation (accept 'inverse correlation')
- (b) Strong correlation (1 mark). Most points lie close to / follow a clear linear trend / the points are clustered tightly around an imaginary line (1 mark)
- (c) The outliers/anomalous results suggest predictions may be unreliable / there may be other variables affecting heat loss that are not accounted for (1 mark)
Explain — 4 marks
A student investigates the relationship between the mass of a ball bearing and the time it takes to fall through a viscous fluid (oil). The student releases ball bearings of different masses from the same height and measures the time taken for each to reach the bottom of the container. The results are plotted on a scatter graph.
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(a) The scatter graph shows a negative correlation between mass and time. What does this tell you about the relationship between these two variables?
[1 mark]
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(b) Explain why a scatter graph is a suitable way to display this data rather than a bar chart.
[1 mark]
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(c) The student notices that one data point lies far away from the general trend of the other points. Explain what this point suggests about that particular measurement and what the student should consider doing.
[2 marks]
Show mark scheme
- (a) Award 1 mark for: As mass increases, time decreases (or equivalent statement showing inverse relationship). Do not accept vague answers like 'they are related'.
- (b) Award 1 mark for: Both variables are continuous/numerical (accept 'quantities') so a scatter graph is appropriate to show correlation. Do not accept 'it shows the data better' without reference to continuous data.
- (c) Award 1 mark for: The point is an outlier/anomalous result (accept 'it doesn't fit the pattern'). Award 1 mark for: It may be a measurement error / the experiment should be repeated for that mass / the result could be discounted (accept any one valid suggestion).
Show — 3 marks
A local shop records the number of customers and the total sales, in pounds, for six days. The table shows the results.
| Number of customers | 15 | 25 | 35 | 45 | 55 | 65 |
|---------------------|----|----|----|----|----|----|
| Sales (£) | 120| 200| 280| 360| 440| 520|
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(a) On the grid, show the point that represents 35 customers and £280 sales.
[1 mark]
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(b) Show that there is positive correlation between the number of customers and the sales.
[2 marks]
Show mark scheme
- (a) Point plotted correctly at (35, 280)
- (b) States that as number of customers increases, sales also increase
- (b) Reference to values from the table or pattern shown in plotted points
GCSE Perfect