In
mathematics and
statistics, deviation is a measure of difference between the observed value of a
variable and some other value, often that variable's
mean
There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value ( magnitude and sign) of a given data set.
For a data set, the '' ari ...
. The
sign
A sign is an Physical object, object, quality (philosophy), quality, event, or Non-physical entity, entity whose presence or occurrence indicates the probable presence or occurrence of something else. A natural sign bears a causal relation to ...
of the deviation reports the direction of that difference (the deviation is positive when the observed value exceeds the reference value). The magnitude of the value indicates the size of the difference.
Types
A deviation that is a difference between an observed value and the ''true value'' of a quantity of interest (where ''true value'' denotes the Expected Value, such as the population mean) is an error.
A deviation that is the difference between the observed value and an ''estimate'' of the true value (e.g. the sample mean; the Expected Value of a sample can be used as an estimate of the Expected Value of the population) is a residual. These concepts are applicable for data at the
interval and
ratio
In mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...
levels of measurement.
Unsigned or absolute deviation
In
statistics, the absolute deviation of an element of a
data set is the
absolute difference
The absolute difference of two real numbers x and y is given by , x-y, , the absolute value of their difference. It describes the distance on the real line between the points corresponding to x and y. It is a special case of the Lp distance for ...
between that element and a given point. Typically the deviation is reckoned from the
central value, being construed as some type of