Types of error
Brook Edgar & Hannah Shuter
Teachers
Contents
Explainer Video
Accurate or Precise
An accurate result from an experiment is one that is very close in value to the actual or true value. For example, if someone recorded by mass and got , this would be very accurate as my actual weight is . Accurate results are obtained when the method is followed exactly, and all equipment is working perfectly.
Precise results from an experiment mean that all of the results are close in value to each other (there is a small range in results), but they may not all be accurate. For example, if someone recorded my mass as the first time, and then the second time and the third time, the results are not accurate as they are far from my actual mass of , but the results are precise, as all of the results are very similar to each other. Precise results are obtained when the method is followed exactly, but there may be an issue with the equipment. For example, the scale used to measure my mass might not read zero before we begin; it might read , so all my results would be too low. This is called a zero error, and it means that all results will be wrong by the same amount. To fix this problem, the scale should be set to read zero before beginning - this is called calibrating the equipment.
Another way to learn this is to imagine a dartboard. If my throws are precise but not accurate, they will all hit the dartboard really close together but nowhere near the bullseye. If my throws are accurate but not precise, they will all be near the bullseye but not close together. If my throws are precise and accurate, they will all hit the dartboard very close together on the bullseye.
Systematic Error
A systematic error is when a result in an experiment is recorded incorrectly due to a problem with the system - with the equipment.
In the example above, when measuring my mass and all recorded values were too low due to a zero error in the scale, this was an example of a systematic error. A problem with the equipment. All values were off by roughly the same amount. A systematic error can not be fixed by repeating the experiment, as every result will still be wrong, since the scale is still off. Systematic errors can only be fixed by either fixing the equipment, in this case, ensuring the scale reads zero before beginning, or by changing the equipment.
Worked Example:
A pupil uses the balance below to measure the mass of an aluminium block. The balance displays the reading shown when nothing is on the balance.
What type of error is this and how could the student fix this error?
Answer:
This is called a systematic error or a zero error.
This can be fixed by either calibrating the equipment -> ensure it reads zero before beginning. Or by subtracting from every measurement as all values recorded will be too high.
Worked Example:
An electric mass balance is switched on and shows a reading of .
An object is placed on it, and the reading is .
What is the true mass of the object?
Answer:
The scale reads instead of when the object is placed on top. This means all objects will have readings too low.
The object would have a mass of if placed on top of the scale when it initially read zero, so the scale increased in value by , but as it initially read and read at the end, the scale increased in value by . Therefore, the actual mass, the true mass of the object, is .
Random Error
A random error is when a mistake is made when recording results in an experiment due to the person. For example, when recording the time it takes for a trolley to go down a ramp using a stopwatch, I may get distracted by my friends and forget to hit the stop button, so the time I record will be too high.
Another example of a random error is measuring the length of a stretched spring with a ruler. If I do not read the scale from eye level, I will get a result that is either too low or too high, depending on whether I am standing above the spring, looking down at the scale on the ruler, or below the spring, looking up. This is called parallax error.
A random error is human error. It is when a value is recorded incorrectly due to a fault with the person. This is why we should always repeat experiments so that when we look at the results, we can see if there are any anomalies caused by random error, and we can then ignore them from our results.
Worked Example:
A toy car is released at the top of a ramp. The time taken to reach the end of the ramp is measured using a stopwatch. This procedure is repeated five times.
Each time, the measured value of time is different.
Suggest a reason why.
Answer:
This is likely due to human error. It is a random error. The person recording the time may have gotten distracted and forgotten to hit the stopwatch when the toy car reached the bottom, or there may be a delay in the time it takes for the person to hit the stopwatch due to their reaction time.
Practice Questions
A student measures the length of a metal rod using a ruler. They repeat the measurement five times and obtain slightly different results each time.
Identify the type of error shown in the student’s results.
Explain why repeating measurements helps reduce the effect of this error.
-> Check out Brook's video explanation for more help.
Answer:
Random error.
Taking multiple readings allows us to notice any anomalies due to human error. They can be ignored from the results, and a mean can be calculated from the remaining values.
A student measures the mass of an empty beaker using a digital balance that reads when nothing is on it.
Identify the type of error present in the balance reading.
Explain how this error will affect all mass measurements taken by the student and how to correct this error.
-> Check out Brook's video explanation for more help.
Answer:
Systematic error / zero error.
All measurements will be wrong by the same amount, giving results that are consistently too high by . The student should zero the balance / press the tare button. Alternatively, they could subtract from each measurement.