AQA GCSE Chemistry Foundation (8462), Foundation tier · Quantitative chemistry › Conservation of mass and chemical measurements
Practise Chemical measurements and uncertainty. 7 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.
Every measurement has some uncertainty. You need to calculate the mean of repeat results, use the range to estimate the uncertainty of the mean, and use uncertainties to compare results. These skills come up in practical and data questions on both papers.
Key facts
Mean = total of results ÷ number of results (leave out anomalies)
Range = highest − lowest
Uncertainty = ± range ÷ 2
Write results as mean ± uncertainty, with a unit
Precise = little spread about the mean
Accurate = close to the true value
Resolution = smallest change an instrument can measure
Repeatable = same person and method; reproducible = different person, method or equipment
Notes
Uncertainty in measurements
Whenever a measurement is made there is always some uncertainty about the result. Repeating it usually gives slightly different values.
Causes include the resolution of the instrument (the smallest change it can show, e.g. a balance that reads to 0.01 g) and random errors, such as judging exactly when a colour changes.
Repeating measurements and calculating a mean reduces the effect of random errors.
Mean, range and uncertainty
diagram
Mean = sum of the results ÷ number of results. Leave out any anomalous results.
Range = highest value − lowest value of the results you used.
Uncertainty = ± (range ÷ 2). The true value is likely to lie between mean − uncertainty and mean + uncertainty.
Worked example: gas volumes of 36.4, 37.0, 36.6 and 36.8 cm3. Mean = 146.8 ÷ 4 = 36.7 cm3. Range = 37.0 − 36.4 = 0.6 cm3. Uncertainty = ± 0.3 cm3. Result: 36.7 ± 0.3 cm3.
Result: 36.7 ± 0.3 cm3. The uncertainty is half the range, measured either side of the mean.
Give the mean to the same number of decimal places as the data.
Key words
diagram
Precise: results are close together, with little spread about the mean. A smaller uncertainty means more precise results.
Accurate: a result that is close to the true value.
The centre is the true value. Close together = precise; close to the centre = accurate.
Repeatable: the same person, using the same method and equipment, gets similar results.
Reproducible: a different person, or a different method or equipment, gets similar results.
Another value agrees with your result if it lies inside the range from mean − uncertainty to mean + uncertainty.
How to answer each type of question
Calculate a mean, leaving out an anomaly
2 marksGrade 4
Spot any result that does not fit the others and leave it out.
Add the remaining results and divide by how many there are.
Round to the same number of decimal places as the data and give the unit.
Example. A student measured the temperature rise in a reaction four times.
Trial
1
2
3
4
Temperature rise in °C
6.2
6.6
9.1
6.4
Calculate the mean temperature rise. Do not include the anomalous result. [2 marks]Show the model answerHide the model answer
(6.2 + 6.6 + 6.4) ÷ 3 (1) = 6.4 °C (1)
Suggest how to reduce the uncertainty
1 to 2 marksGrade 5
Name a specific change, such as a balance or measuring cylinder with a higher resolution.
Say why it helps: the reading is closer to the true value, or repeat results are closer together.
Example. A student used a balance that reads to the nearest 0.1 g to weigh about 0.5 g of magnesium ribbon. Suggest how the student could reduce the uncertainty in the mass. Give a reason. [2 marks]
Show the model answerHide the model answer
Use a balance with a higher resolution, e.g. one that reads to 0.01 g (1). The uncertainty in each reading is then much smaller compared with the mass being measured (1).
Don’t lose marks
Including the anomalous result in the mean or the range.
Giving the whole range as the uncertainty instead of half of it.
Leaving out the ± sign or the unit.
Mixing up precise (close together) and accurate (close to the true value).
Giving the mean to more decimal places than the data, e.g. 36.733 cm3 from readings to 0.1 cm3.
More tips
Memory tricks
Uncertainty is half the spread: find the range, then halve it.
Sense check: the mean must lie between the lowest and highest values you used.
Think of darts: a tight group is precise; a group around the bullseye is accurate. You can be precise without being accurate.
Draw a quick number line from mean − uncertainty to mean + uncertainty to see whether another value falls inside.
Exam technique
Show the range as its own line of working: it is often worth a mark on its own.
When comparing results, quote numbers: the ranges, and whether a value lies inside them.
Use 'precise', 'accurate', 'repeatable' and 'reproducible' with their exact meanings, and avoid vague words such as 'reliable'.
What each grade needs
What you need to be able to do, from the first marks up to the top grade.
Grade 3
Calculate a mean from repeat readingsAdd up the results, leaving out any anomalous ones, and divide by how many you added.
Grade 4
Find the range of a set of resultsRange = highest value − lowest value.
Grade 5
Identify an anomalous resultA result that clearly does not fit the pattern of the others; leave it out of the mean.
Quick recall
Cover the answers and test yourself. The app has these as flashcards that come back just before you'd forget them.
A student measured the temperature of a solution three times: 21.5 °C, 22.0 °C and 21.0 °C. Calculate the mean temperature.
21.5 °C
Sample questions
Written for this site in the style of AQA exam questions. They are not taken from real past papers.
Question 1Easy4 marks
Every measurement made with an instrument has some uncertainty.
(a) A balance shows the mass of a sample as 12.47 g. What is the resolution of the balance? Tick (✓) one box.[1]
0.01 g
0.1 g
1 g
12.47 g
(b) Give one reason why scientists repeat a measurement several times and calculate a mean.[1]
(c) A student measured the temperature of a solution three times: 21.5 °C, 22.0 °C and 21.0 °C. Calculate the mean temperature.[1]
(d) The uncertainty in the mean can be estimated as half the range of the readings. Calculate the uncertainty in the mean temperature.[1]
Show the answer and mark scheme
(a)Answer: 0.01 g
(b)
a single reading may be unusually high or low (anomalous) / repeating reduces the effect of random errors / repeating shows whether the results are repeatable
(c)Answer: 21.5 °C
21.5 (°C)
(d)Answer: ± 0.5 °C
range = 22.0 − 21.0 = 1.0 (°C), so the uncertainty is ± 0.5 (°C)
Question 2Medium5 marks
Whenever a measurement is made there is some uncertainty in the result.
(a) A student needs to measure 25.0 cm3 of sodium hydroxide solution as accurately as possible. Which piece of apparatus should the student use? Tick (✓) one box.[1]
Beaker
Conical flask
Measuring cylinder
Volumetric pipette
(b) The student measured a temperature using a thermometer with a resolution of 0.5 °C. What is meant by the resolution of a measuring instrument?[1]
(c) The student’s balance was not set to zero. It read 0.12 g with nothing on it. The student used it to measure the masses of several samples. Name the type of error this causes and describe its effect on the measured masses.[2]
(d) Explain why finding the mass of a sample by difference (weighing a container before and after adding the sample) removes this error.[1]
Show the answer and mark scheme
(a)Answer: Volumetric pipette
(b)
the smallest change in the quantity that the instrument can measure / the size of the smallest scale division
(c)
systematic error / zero error
every mass reading is 0.12 g too high / all readings are wrong by the same amount
(d)
the extra 0.12 g is in both readings, so it cancels out when one reading is subtracted from the other