Uncertainty in a Measurement and Where It Comes From
Every measured value carries a range, and quoting the value without it says nothing about whether two results agree. Some of that range is found by repeating the measurement and the rest is read off the equipment.
What a learner can do afterwards
- Estimates an uncertainty from repeated readings and states the number of readings used
- Estimates an uncertainty from a manufacturer's tolerance when repeating is not possible
- Distinguishes a random contribution from a systematic one and names an experiment that would reveal each
- Quotes a result with a matched number of significant figures in the value and its uncertainty
1 · Read
You never get to report a bare number. Every measurement carries a small range, and you must quote it, or nobody can tell whether two results agree. Precision means your repeats agree with each other. Accuracy means they sit near the truth.
You measure a table five times and get 120.1, 120.3, 120.2, 120.3 and 120.1 cm. Order them, then subtract the lowest from the highest: 120.3 minus 120.1 is 0.2 cm. Report half of that range, plus or minus 0.1 cm, and always state that it came from 5 readings.
Some things you can measure only once, like a flask you may fill a single time. Then your uncertainty comes from the tolerance the maker printed on the glassware. Learn the two kinds of error: scatter around the middle is random and repeats reveal it, while a steady push one way is systematic, like a scale that always reads 2 kg heavy, and only a known standard reveals that.
Quote the value and its uncertainty so their digits stop together, as in 120.2 cm plus or minus 0.1 cm. Extra digits claim knowledge your readings never gave you.
Quote every result with its range, and let repeats, tolerances and a known standard each play their part.
More to read
4 Ways to Calculate Precision
When you measure something more than once, the readings almost never come out exactly the same. Precision is about how close those repeated readings are to each other. A good measuring tool gives nearly the same value every time you use it. Think of stepping on a bathroom scale five times in a row. If it shows almost the same weight each time, it is precise.
One simple way to describe the spread of your readings is to calculate the range. First, write all of your readings down in order from smallest to largest. This helps you make sure you do not miss any of them. Then find the highest reading and the lowest reading. The range is the highest value minus the lowest value. For example, if you measure the length of a table five times and get 120.1 cm, 120.3 cm, 120.2 cm, 120.3 cm, and 120.1 cm, the highest value is 120.3 cm and the lowest is 120.1 cm, so the range is 0.2 cm.
That range tells you something important. A small range means your readings are clustered tightly together, so you can trust that they agree. A large range means the readings are scattered, so a single reading does not tell you much. In science, half of that range is often used as a simple estimate of the uncertainty, because it says how far a typical reading sits from the middle of the group.
You can also look at how far each reading sits from the average of all the readings. Find the average first, then subtract it from each reading to see the gap. Small gaps mean high precision. This idea leads to fancier measures like standard deviation, which is just a more careful way of averaging those gaps.
Remember, precision is not the same as accuracy. A tool can be very precise but still be wrong every time, like a scale that always reads 2 kg too heavy. That is why scientists repeat measurements and also check their equipment against a known standard.
2 · Watch
En anglaisTake it off screen
Where it sits
Optional connections
This opens up
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.