AQA · GCSE · Combined Science
Course version: 8464 · Version from Sept 2018
Use the range of a set of measurements about the mean as a measure of…
Full specification wording
Chemical measurements: use the range of a set of measurements about the mean as a measure of uncertainty.
The range describes how far apart the smallest and largest readings are, and it gives a quick measure of how uncertain a mean value is.
Checked against the AQA 8464 specification (opens in a new tab) on .
- Point 3 of 3
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
The range describes how far apart the smallest and largest readings are, and it gives a quick measure of how uncertain a mean value is. To use it, first calculate the mean of the repeated measurements, then subtract the smallest reading from the largest to find the range. The uncertainty is estimated as half the range, written with a ± sign after the mean. For instance, if four titres are 23.80 cm³, 24.00 cm³, 23.90 cm³ and 24.10 cm³, the mean is 23.95 cm³ and the range is 0.30 cm³, so the uncertainty is ±0.15 cm³. A small range relative to the mean indicates precise, repeatable measurements; a large range warns that the mean is less trustworthy and that technique or apparatus may need checking.
What earns the marks
- Identifies the largest and smallest values in a set of repeated measurements.
- Calculates the range by subtracting the smallest value from the largest value.
- Calculates the mean of the measurements before quoting the uncertainty.
- Estimates uncertainty as half the range and expresses the result as mean ± uncertainty with correct units.
- Interprets a small range as indicating greater precision and a large range as indicating greater uncertainty.
- Applies the method to data from a practical context, such as titration volumes or temperature changes.
Common mistakes and how to put them right
Reporting the range as the uncertainty rather than half the range.
Put it right: Halve the range to estimate uncertainty about the mean.
Forgetting to calculate the mean first and attaching the uncertainty to a single reading.
Put it right: The uncertainty describes the mean of the set.
Mixing units or decimal places between the mean and the uncertainty.
Put it right: Keep both in the same unit and to the same precision.
Exam tips
- Write the range calculation explicitly, for example 24.10 − 23.80 = 0.30 cm³, before halving it.
- State the final answer in the form mean ± uncertainty with the unit given once, such as 23.95 ± 0.15 cm³.
- If asked to comment, link the size of the range to precision or reliability rather than simply restating the number.
Try the lesson
The start of the Chemical measurements: use the range of a set of measurements about the mean as a measure of uncertainty. lesson, made from checked teaching notes for this specification point.
Have a go first
A student records four repeat measurements of the volume of gas produced: 24 cm³, 26 cm³, 25 cm³ and 25 cm³. The student uses the range of these measurements about the mean as a measure of uncertainty. What is the uncertainty in these measurements?
Listen
The range describes how far apart the smallest and largest readings are, and it gives a quick measure of how uncertain a mean value is. To use it, first calculate the mean of the repeated measurements, then subtract the smallest reading from the largest to find the range. The uncertainty is estimated as half the range, written with a ± sign after the mean. For instance, if four titres are 23.80 cm³, 24.00 cm³, 23.90 cm³ and 24.10 cm³, the mean is 23.95 cm³ and the range is 0.30 cm³, so the uncertainty is ±0.15 cm³. A small range relative to the mean indicates precise, repeatable measurements; a large range warns that the mean is less trustworthy and that technique or apparatus may need checking. A strong answer earns marks for these points. Identifies the largest and smallest values in a set of repeated measurements. Calculates the range by subtracting the smallest value from the largest value. Calculates the mean of the measurements before quoting the uncertainty. Estimates uncertainty as half the range and expresses the result as mean ± uncertainty with correct units. A common slip: Reporting the range as the uncertainty rather than half the range. Instead, halve the range to estimate uncertainty about the mean. Exam tip: Write the range calculation explicitly, for example 24.10 − 23.80 = 0.30 cm³, before halving it.
Key words
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Range as a measure of spread
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Uncertainty about a mean value
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Precision and repeatability of measurements
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Evaluating experimental data
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See every definition
- Range as a measure of spread
- Describes how far apart the smallest and largest readings are, found by subtracting the smallest reading from the largest.
- Uncertainty about a mean value
- Estimated as half the range and written with a ± sign after the mean of the repeated measurements.
- Precision and repeatability of measurements
- A small range relative to the mean indicates precise, repeatable measurements, while a large range warns that technique or apparatus may need checking.
- Evaluating experimental data
- A large range warns that the mean is less trustworthy, so technique or apparatus may need checking.
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