In probability theory

Probability theory

Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...

 and statistics

Statistics

Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

, the relative standard deviation (RSD or %RSD) is the absolute value

Absolute value

In mathematics, the absolute value |a| of a real number a is the numerical value of a without regard to its sign. So, for example, the absolute value of 3 is 3, and the absolute value of -3 is also 3...

 of the coefficient of variation

Coefficient of variation

In probability theory and statistics, the coefficient of variation is a normalized measure of dispersion of a probability distribution. It is also known as unitized risk or the variation coefficient. The absolute value of the CV is sometimes known as relative standard deviation , which is...

. It is often expressed as a percentage. A similar term that is sometimes used is the relative variance which is the square of the coefficient of variation. Also, the relative standard error is a measure of a statistical estimate's reliability obtained by dividing the standard error

Standard error (statistics)

The standard error is the standard deviation of the sampling distribution of a statistic. The term may also be used to refer to an estimate of that standard deviation, derived from a particular sample used to compute the estimate....

 by the estimate; then multiplied by 100 to be expressed as a percentage.

The relative standard deviation is widely used in analytical chemistry

Analytical chemistry

Analytical chemistry is the study of the separation, identification, and quantification of the chemical components of natural and artificial materials. Qualitative analysis gives an indication of the identity of the chemical species in the sample and quantitative analysis determines the amount of...

 to express the precision and repeatability of an assay

Assay

An assay is a procedure in molecular biology for testing or measuring the activity of a drug or biochemical in an organism or organic sample. A quantitative assay may also measure the amount of a substance in a sample. Bioassays and immunoassays are among the many varieties of specialized...

.

100 × [(standard deviation of array X)/ (average of array X)] = relative standard deviation expressed as a percentage