Chemical measurements
Lajoy Tucker
Teacher
Contents
Understanding Measurement and Uncertainty
In science, every measurement involves a degree of uncertainty – no measurement is ever perfectly exact.
This is because of limitations in equipment, human error, or small variations in the conditions of the experiment.
Recognising and estimating uncertainty is an important part of reporting scientific data.
Key Point:
Uncertainty does not mean the result is wrong – it shows the range of possible values within which the true value is likely to lie.
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Calculating Uncertainty
When multiple measurements are taken, the results usually form a distribution around a mean (average) value.
The mean gives the best estimate of the true value.
Some results may be slightly higher or lower than the mean due to random variation.
Example:
If you measure the temperature change in a reaction five times and get
Then the mean is:
The range shows how much the measurements vary:
For the example above:
To express uncertainty, we use half the range on either side of the mean:
So here:
The final result can be written as:
This means the true value is likely to lie between
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Check for Understanding
Recall
a) What is meant by uncertainty in a scientific measurement?
Answer:
a) Uncertainty is the range of possible values within which the true value is likely to lie.
b) State one reason why measurements may contain uncertainty.
Answer:
b) Accept one of: limitations of equipment, human error, or small variations in experimental conditions.
c) What statistical value is used to give the best estimate of the true value when several measurements are taken?
Answer:
c) The mean (average).
Application
d) A student records the following temperatures (°C): 20.1, 20.3, 20.2, 20.0, 20.4
Answer:
d) Mean = (20.1 + 20.3 + 20.2 + 20.0 + 20.4) ÷ 5
Mean = 20.2 °C.
e) Using the data in question (d), calculate the uncertainty in the measurement and report the final result.
Answer:
e) Range = highest − lowest = 20.4 − 20.0 = 0.4 °C
Uncertainty = ±(0.4 ÷ 2) = ±0.2 °C
Final result: 20.2 ± 0.2 °C.
f) Explain why scientists report results with uncertainty.
Answer:
f) Scientists report uncertainty to show the possible range of values in which the true value may lie and to reflect the limitations of measurements.