Chemical measurements
Lajoy Tucker
Teacher
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.
No answer provided.
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
No answer provided.
Practice Question:
A student measures the mass of a sample five times (in grams):
2.30, 2.28, 2.32, 2.29, 2.31
Calculate the mean and the uncertainty.
Answer:
Mean = (2.30 + 2.28 + 2.32 + 2.29 + 2.31) ÷ 5 = 2.30 g
Range = 2.32 − 2.28 = 0.04 g
Uncertainty = ±(0.04 ÷ 2) = ±0.02 g
Final result: 2.30 ± 0.02 g