Explain — 3 marks
A student carried out an experiment to measure the time taken for a ball to roll down a ramp. She repeated the measurement 5 times and obtained the following results: 2.1 s, 2.3 s, 2.0 s, 2.2 s, and 2.4 s. She calculated the mean as 2.2 s and the range as 0.4 s.
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(a) Explain why the student should use the mean rather than a single measurement to represent her results.
[1 mark]
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(b) Explain what the range of 0.4 s tells us about the precision of the student's measurements.
[1 mark]
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(c) Explain how the student could improve the reliability of her results using the concepts of averages and spread.
[1 mark]
Show mark scheme
- (a) The mean reduces the effect of random errors / anomalies in individual measurements
- (a) OR: A single measurement may not be representative of the true value
- (a) OR: The mean gives a more reliable / accurate estimate by combining all the data
- (b) The range shows the spread of the data / difference between highest and lowest values
- (b) A range of 0.4 s indicates the measurements are not very precise
- (b) OR: There is significant variation in the results, suggesting random errors were present
- (c) Take more repeat measurements to increase the sample size
- (c) This would reduce the effect of random errors on the mean
- (c) OR: A larger number of repeats would give a more reliable average / reduce the range
Calculate — 4 marks
A physics student investigates the extension of a spring under different loads. They measure the extension (in mm) for each load five times to check the reliability of their results. The five measurements for a 2 N load are: 24 mm, 26 mm, 25 mm, 27 mm, and 24 mm.
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(a) Calculate the mean extension for the 2 N load.
[1 mark]
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(b) Calculate the range of the extension measurements.
[1 mark]
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(c) The student's apparatus has a resolution of ±0.5 mm. Using your answers from parts (a) and (b), explain whether the spread of results is significant compared to the resolution of the apparatus.
[2 marks]
Show mark scheme
- (a) Mean = (24 + 26 + 25 + 27 + 24) ÷ 5 = 25.2 mm (or 126 ÷ 5 = 25.2 mm)
- (b) Range = 27 - 24 = 3 mm
- (c) Range of 3 mm is greater than ±0.5 mm (or 3 mm is larger than twice the resolution)
- (c) Therefore the spread is significant / indicates poor precision / suggests random errors are present / results are not reliable
Explain — 3 marks
A student investigates the time taken for a ball to roll down a ramp from rest. They repeat the experiment 10 times and record the following times in seconds: 2.1, 2.3, 2.1, 2.2, 2.4, 2.1, 2.2, 2.3, 2.2, 2.5. The mean time is 2.24 seconds and the range is 0.4 seconds.
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(a) Calculate the mean time for the ball to roll down the ramp.
[1 mark]
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(b) Explain why the range alone is not a sufficient measure of spread to evaluate the precision of this experiment.
[2 marks]
Show mark scheme
- (a) Mean = 2.24 seconds (or equivalent calculation showing sum of 22.4 divided by 10)
- (b) Range only uses the highest and lowest values, so it does not show how the data is distributed between these extremes
- (b) A large range could occur due to a single anomalous result, whereas most values might be clustered close together, giving false impression of poor precision
Evaluate — 4 marks
A student carried out an experiment to measure the time taken for a ball to roll down a ramp. They repeated the measurement 5 times and obtained the following results in seconds: 2.1, 2.3, 2.2, 2.1, 2.4
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(a) Calculate the mean time for the ball to roll down the ramp.
[1 mark]
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(b) Identify the range of the measurements.
[1 mark]
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(c) Evaluate whether the student's results show good repeatability. Justify your answer using the data.
[2 marks]
Show mark scheme
- (a) Mean = (2.1 + 2.3 + 2.2 + 2.1 + 2.4) ÷ 5 = 2.2 s (or 11.1 ÷ 5 = 2.22 s)
- (b) Range = 2.4 - 2.1 = 0.3 s
- (c) The results show good repeatability because the range (0.3 s) is small / most values are close to the mean
- (c) All values fall within a narrow range (2.1 to 2.4 s) showing consistent measurements / the spread is small compared to the mean value
Calculate — 2 marks
A teacher records the scores of five students in a mathematics quiz. The scores are: 12, 15, 8, 15, and 10.
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(a) Calculate the mean score.
[1 mark]
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(b) Calculate the range of the scores.
[1 mark]
Show mark scheme
- (a) (12 + 15 + 8 + 15 + 10) ÷ 5 = 12 OR equivalent method
- (a) 12
- (b) 15 − 8
- (b) 7
GCSE Perfect