# Systematic Error & Random Error

Show/Hide Sub-topics (Measurement | O Level Physics)
Show/Hide Sub-topics (Measurement | A Level Physics)

## Systematic Errors

Systematic errors are errors of measurements in which the measured quantities are displaced from the true value by fixed magnitude and in the same direction.

Example of systematic error

• Zero error
• Parallax error – viewing consistently from the wrong angle for all readings
• Environmental conditions – Background radiation in the measurement of radioactive decay.

Systematic errors cannot be eliminated by averaging or by statistical means.

### Ways To Avoid Systematic Errors

Systematic errors can be avoided by

• Checking for zero error before taking readings
• Plotting a graph. If the graph does not cut the expected intercept, the shift is probably due to systematic error.

## Random Errors

Random errors are errors of measurements in which the measured quantities differ from the mean value with different magnitudes and directions.

• Always a good practice to take repeated measurements across different regions of wire when determining the diameter of a thin piece of wire as it may not be uniform

### Sources of Random Errors

• Arise from parallax error when an observer reads a scale from an inconsistent direction
• Variation in environmental conditions
• Irregularity of the quantity being measured as certain quantities by nature do not follow a regular pattern
• Limitation of the equipment as certain equipment may be so sensitive that it can detect even the slightest variation on the signals( not a good thing if a general reading is what you want)

### Ways To Reduce Random Errors

• Taking repeated measurements to obtain an average value
• Plotting a graph to establish a pattern and obtaining the line or curve of best fit. In this way, the discrepancies or errors are reduced
• Maintaining good experimental technique (e.g. reading from a correct position)

## Worked Examples

### Example 1

You perform an experiment to measure the boiling point of water using a thermometer that has not been calibrated and consistently reads 2°C higher than the actual temperature. Is this an example of systematic or random error? Explain.

This is an example of systematic error because the error consistently occurs in the same direction due to the uncalibrated thermometer. The thermometer adds an extra 2°C to every measurement, affecting the accuracy of the boiling point measurement.

### Example 2

During a series of measurements of the acceleration due to gravity using a simple pendulum, you observe that the measurements vary slightly around the accepted value each time you perform the experiment. What type of error is this, and how can it be minimized?

This is an example of random error as the measurements vary in both magnitude and direction from one trial to the next. These variations could be due to slight differences in initial conditions, air currents, or timing precision. Random errors can be minimized by increasing the number of observations and calculating the average value.

### Example 3

A lab group measures the mass of a sample with a balance that they didn’t realize was zeroed incorrectly, always showing a mass 0.5g less than the actual mass. Identify the type of error and suggest a method to correct it in future experiments.

This is an example of systematic error caused by the balance being zeroed incorrectly. The error consistently occurs in the same direction, affecting the accuracy of the mass measurements. To correct this error in future experiments, the balance should be properly calibrated before use, ensuring it reads zero when empty.

### Example 4

In measuring the period of a pendulum, different students time the period using their own stopwatches and their reaction times cause slight differences in the recorded times. What type of error does this scenario illustrate, and what strategy could reduce its impact?

This scenario illustrates random error, arising from the students’ varying reaction times when starting and stopping their stopwatches. These errors affect the precision of the period measurements. To reduce the impact of this type of error, multiple measurements should be made and the average period should be calculated, or a more precise timing method should be used.

### Example 5

A researcher measuring the pH of a solution uses pH indicator strips that change color to indicate pH level. However, the strips are old and consistently indicate a pH that is 0.3 units too acidic. Is this a systematic or random error, and how should the researcher proceed?

This is an example of systematic error because the outdated pH strips consistently indicate a pH value that is 0.3 units too acidic. The error is systematic as it affects the accuracy of the pH measurements in a predictable way. To address this issue, the researcher should use fresh, properly stored pH indicator strips or more reliable pH measurement methods, such as a calibrated pH meter.

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