Systematic and Random Errors
Brook Edgar
Teacher
Explainer Video
Types of Error
Random errors
These cause readings to be spread about the true value, due to results varying in an unpredictable way from one measurement to the next.
An example of a random error is getting distracted when timing the free fall of a ball. To reduce this, we should use light gates to minimise human error.
The effect of random errors can be reduced by repeating measurements and calculating the average, ensuring to ignore any anomalous results.
Systematic errors
These cause readings to differ from the true value by a consistent amount each time a measurement is made.
Sources of systematic error can include the environment, methods of observation or instruments used.
Systematic errors cannot be dealt with by repeating measurements and averaging.
If a systematic error is suspected, data collection should be repeated using a different technique or equipment, and the results compared. An example of a systematic error is a zero error on a balance - to avoid this, always check the scale reads zero before using it.
Accuracy and Precision
Accuracy is how close your measurement is to the true value. It is obtained by using well-calibrated equipment, with no systematic errors.
Precision of a measurement is the degree of exactness of the measurement. Precise readings are not necessarily accurate readings, because systematic errors could make precise readings higher or lower than the actual value. For example, when recording the volume of a bottle of water, it is more precise to use a measuring cylinder than a beaker because of its higher resolution. As shown below, the resolution of the measuring cylinder is whereas, the resolution of the beaker is .
Remember: When recording volume, ensure to read from eye level from the bottom of the meniscus (the bottom of the curve of the liquid) to avoid parallax error. This is also important to note when taking readings from thermometers.
Worked Example
The sealed radioactive source is used in schools.
The source emits gamma, alpha and beta radiation. A pupil wants to investigate the inverse square law and starts by measuring the count rate for background radiation.
1. State two procedures to reduce risk when using this source.
2. Explain how they will eliminate systematic errors in the measurement and how to reduce the percentage uncertainty in their recorded value.
Answer:
1. Procedures to reduce risk:
Use tongs when handling the source to keep it as far away as possible from you.
Remove the source from the room when not in use and keep it in a lead-lined box.
Stand behind a lead screen when carrying out the experiment to shield yourself.
Never point the source at anyone.
2. Suitable procedures to eliminate systematic errors:
Remove all radioactive sources from the room before measuring the count rate of the source and the background count rate.
Measure the background count rate before having the source in the room.
Check that the counter and stopwatch have no zero error.
To reduce percentage uncertainty, record the background count rate for a long time - around minutes minimum.
Practice Questions
A horizontal tube, T, is connected to a vertical glass tube.
Explain how a student can check that the glass tube is vertical.
-> Check out Brook's video explanation for more help.
Answer:
Assume the floor is horizontal.
Place a set square on the floor to find the vertical, and then place a ruler against the side of the vertical set square to check if the vertical tube aligns with the ruler.
Or use a plumbline.
A student uses a sealed source to investigate the inverse square law of radiation. They begin by measuring the background count rate.
1. State and explain how to eliminate systematic errors in their results.
2. State and explain how to reduce the percentage uncertainty in the recorded value of background count rate.
-> Check out Brook's video explanation for more help.
Answer:
1. Check that there are no zero errors in the stopwatch and Geiger tube. Record all measurements on the same day, ensuring the source is not in the room when recording the background count rate.
2. Measure the background rate for a long time; this gives a lower uncertainty.