Errors are normally classified in three categories: systematic errors, random errors, and blunders.

Systematic Errors

Systematic errors are due to identified causes and can, in principle, be eliminated. Errors of this type result in measured values that are consistently too high or consistently too low. Systematic errors may be of four kinds:

1. Instrumental. For example, a poorly calibrated instrument such as a thermometer that reads 102 oC when immersed in boiling water and 2 oC when immersed in ice water at atmospheric pressure. Such a thermometer would result in measured values that are consistently too high.

2. Observational. For example, parallax in reading a meter scale.

3. Environmental. For example, an electrical power ìbrown outî that causes measured currents to be consistently too low.

4. Theoretical. Due to simplification of the model system or approximations in

the equations describing it. For example, if your theory says that the temperature of the surrounding will not affect the readings taken when it actually does, then this factor will introduce a source of error.

Random Errors

Random errors are positive and negative fluctuations that cause about one-half of the measurements to be too high and one-half to be too low. Sources of random errors cannot always be identified. Possible sources of random errors are as follows:

1. Observational. For example, errors in judgment of an observer when reading the scale of a measuring device to the smallest division.

2. Environmental. For example, unpredictable fluctuations in line voltage, temperature, or mechanical vibrations of equipment.

Random errors, unlike systematic errors, can often be quantified by statistical analysis, therefore, the effects of random errors on the quantity or physical law under investigation can often be determined.

Example to distinguish between systematic and random errors is suppose that you use a stop watch to measure the time required for ten oscillations of a pendulum. One source of error will be your reaction time in starting and stopping the watch. During one measurement you may start early and stop late; on the next you may reverse these errors. These are random errors if both situations are equally likely. Repeated

measurements produce a series of times

that are all slightly different. They vary in random vary about an average value.

If a systematic error is also included for example, your stop watch is not starting from zero, then your measurements will vary, not about the average value, but about a displaced value.


A final source of error, called a blunder, is an outright mistake. A person may record a wrong value, misread a scale, forget a digit when reading a scale or recording a measurement, or make a similar blunder. These blunder should stick out like sore thumbs if we make multiple measurements or if one person checks the work of another. Blunders should not be included in the analysis of data.