Random errors are error

Error

The word error entails different meanings and usages relative to how it is conceptually applied. The concrete meaning of the Latin word "error" is "wandering" or "straying". Unlike an illusion, an error or a mistake can sometimes be dispelled through knowledge...

s in measurement

Measurement

Measurement is the process or the result of determining the ratio of a physical quantity, such as a length, time, temperature etc., to a unit of measurement, such as the metre, second or degree Celsius...

 that lead to measurable values being inconsistent when repeated measures of a constant attribute or quantity

Physical quantity

A physical quantity is a physical property of a phenomenon, body, or substance, that can be quantified by measurement.-Definition of a physical quantity:Formally, the International Vocabulary of Metrology, 3rd edition defines quantity as:...

 are taken. The word random indicates that they are inherently unpredictable

Predictability

Predictability is the degree to which a correct prediction or forecast of a system's state can be made either qualitatively or quantitatively.-Predictability and Causality:...

, and have null expected value

Expected value

In probability theory, the expected value of a random variable is the weighted average of all possible values that this random variable can take on...

, namely, they are scattered about the true value, and tend to have null arithmetic mean

Arithmetic mean

In mathematics and statistics, the arithmetic mean, often referred to as simply the mean or average when the context is clear, is a method to derive the central tendency of a sample space...

 when a measurement is repeated several times with the same instrument. All measurements are prone to random error.

Random error is caused by unpredictable fluctuations in the readings of a measurement apparatus, or in the experimenter's interpretation of the instrumental reading; these fluctuations may be in part due to interference of the environment with the measurement process.

The concept of random error is closely related to the concept of precision

Accuracy and precision

In the fields of science, engineering, industry and statistics, the accuracy of a measurement system is the degree of closeness of measurements of a quantity to that quantity's actual value. The precision of a measurement system, also called reproducibility or repeatability, is the degree to which...

. The higher the precision of a measurement instrument, the smaller the variability (standard deviation

Standard deviation

Standard deviation is a widely used measure of variability or diversity used in statistics and probability theory. It shows how much variation or "dispersion" there is from the average...

) of the fluctuations in its readings.

Systematic versus random error

Measurement errors can be split into two components: random error and systematic error

Systematic error

Systematic errors are biases in measurement which lead to the situation where the mean of many separate measurements differs significantly from the actual value of the measured attribute. All measurements are prone to systematic errors, often of several different types...

.

Random error is always present in a measurement. It is caused by inherently unpredictable fluctuations in the readings of a measurement apparatus or in the experimenter's interpretation of the instrumental reading.

Whereas, systematic errors are predictable, and typically constant or proportional to the true value. If the cause of the systematic error can be identified, then it can usually be eliminated. Systematic errors are caused by imperfect calibration of measurement instruments or imperfect methods of observation

Observation

Observation is either an activity of a living being, such as a human, consisting of receiving knowledge of the outside world through the senses, or the recording of data using scientific instruments. The term may also refer to any data collected during this activity...

, or interference of the environment

Surroundings

Surroundings are the area around a given physical or geographical point or place. The exact definition depends on the field. Surroundings can also be used in geography and mathematics, as well as philosophy, with the literal or metaphorically extended definition.In thermodynamics, the term is used...

 with the measurement process, and always affect the results of an experiment

Experiment

An experiment is a methodical procedure carried out with the goal of verifying, falsifying, or establishing the validity of a hypothesis. Experiments vary greatly in their goal and scale, but always rely on repeatable procedure and logical analysis of the results...

in a predictable direction. Incorrect zeroing of an instrument leading to a zero error is an example of systematic error in instrumentation.