AQA · GCSE · Combined Science
Course version: 8464 · Version from Sept 2018
Represent the distribution of results and make estimations of uncertainty
Full specification wording
Chemical measurements: represent the distribution of results and make estimations of uncertainty
When a measurement is repeated, the results scatter about a central value.
Checked against the AQA 8464 specification (opens in a new tab) on .
- Point 2 of 3
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
When a measurement is repeated, the results scatter about a central value. Representing that distribution means tabulating every reading, then plotting a suitable graph such as a dot plot, tally chart or histogram so the spread is visible. The mean is calculated by adding the readings and dividing by how many there are. Uncertainty is then estimated from the spread: a simple estimate is half the range, found by subtracting the smallest reading from the largest and halving the difference. For example, titre volumes 24.10 cm³, 24.30 cm³ and 24.20 cm³ have a range of 0.20 cm³, so the estimated uncertainty is ±0.10 cm³ and the result is quoted as 24.20 ± 0.10 cm³. A wide distribution signals imprecise technique; a narrow one suggests reliable measurements.
What earns the marks
- Records each repeat measurement accurately, including correct units and a consistent number of decimal places.
- Calculates the mean by summing the readings and dividing by the number of readings.
- Finds the range by subtracting the smallest reading from the largest reading.
- Estimates uncertainty as half the range and quotes the final result with a ± value and unit.
- Represents the distribution using an appropriate method, such as a dot plot, tally chart or histogram, with a sensible scale and labelled axes.
- Comments on what the spread of results indicates about the precision or reliability of the measurements.
Common mistakes and how to put them right
Dividing by the wrong number when finding the mean, for example dividing by the number of readings minus one.
Put it right: Divide by the total number of readings taken.
Quoting the range itself as the uncertainty.
Put it right: The simple estimate of uncertainty is half the range.
Drawing a histogram with unequal class widths and ignoring frequency density.
Put it right: Use frequency density on the y-axis when class widths differ, or choose equal class widths.
Exam tips
- Show the mean calculation and the range calculation separately so the examiner can award method credit even if the final value slips.
- Keep units throughout and give the uncertainty the same unit and decimal precision as the mean.
- When asked to represent a distribution, label both axes and choose a scale that uses most of the grid without distorting the spread.
Try the lesson
The start of the Chemical measurements: represent the distribution of results and make estimations of uncertainty lesson, made from checked teaching notes for this specification point.
Have a go first
A student measures the mass of a product three times. The recorded masses are 4.2 g, 4.6 g and 4.4 g. The mean mass is 4.4 g. What is the estimated uncertainty of this mean value?
Listen
When a measurement is repeated, the results scatter about a central value. Representing that distribution means tabulating every reading, then plotting a suitable graph such as a dot plot, tally chart or histogram so the spread is visible. The mean is calculated by adding the readings and dividing by how many there are. Uncertainty is then estimated from the spread: a simple estimate is half the range, found by subtracting the smallest reading from the largest and halving the difference. For example, titre volumes 24.10 cm³, 24.30 cm³ and 24.20 cm³ have a range of 0.20 cm³, so the estimated uncertainty is ±0.10 cm³ and the result is quoted as 24.20 ± 0.10 cm³. A wide distribution signals imprecise technique; a narrow one suggests reliable measurements. A strong answer earns marks for these points. Records each repeat measurement accurately, including correct units and a consistent number of decimal places. Calculates the mean by summing the readings and dividing by the number of readings. Finds the range by subtracting the smallest reading from the largest reading. Estimates uncertainty as half the range and quotes the final result with a ± value and unit. A common slip: Dividing by the wrong number when finding the mean, for example dividing by the number of readings minus one. Instead, divide by the total number of readings taken. Exam tip: Show the mean calculation and the range calculation separately so the examiner can award method credit even if the final value slips.
Key words
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Mean
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Range
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Uncertainty
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Distribution
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See every definition
- Mean
- A central value calculated by adding the readings and dividing by how many there are.
- Range
- Found by subtracting the smallest reading from the largest reading.
- Uncertainty
- Estimated from the spread, with a simple estimate being half the range.
- Distribution
- The spread of results, represented by tabulating every reading and plotting a suitable graph such as a dot plot, tally chart or histogram.
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