# Deviation

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Related to Deviation: standard deviation, Average deviation

## deviation

[‚dēv·ē′ā·shən]## Deviation

in artillery, an accidental phenomenon not allowed for in the laws of dispersion, by which shells (bullets) veer away from the mean trajectory expected under the given firing conditions. Causes of deviation may be the mechanical disruption of the movement of the shell in the bore (for example, separation of the shell from the rifling grooves) or in the air (for example, a defect in the stabilizer fins or other parts), as well as a chance sharp change in weather conditions during the flight of the shell.

## Deviation

in biology, a variety of phylembryogenesis in which a change in the development of an organ arises in the middle stages of its formation and results in a change in the structure of the organ in the adult organism, compared with the same organ in its ancestors. For example, in the middle stages of development the epidermal part of the scale buds of reptiles undergoes keratinization, not ossification (as in sharks). The term “deviation” was introduced by the German scientist F. Müller (1864).

## Deviation

the most common measure of dispersion, that is, deviation from the mean, in mathematical statistics and theory of probability. In the statistical sense, deviation

is the arithmetic mean of the squares of the deviations of the values *Xi* from their arithmetic mean

In the theory of probability the deviation (variance) of a random variable *X* is called the expected value E(X - m_{x})^{2} of the square of the deviation of *X* from its expected value m_{x} =E(X). The deviation of a random variable *X* is denoted by *D(X*) or by σ^{2}). The square root of the deviation (that is, if the deviation is σ^{2}) is called standard deviation.

For a random variable *X* with continuous probability distribution, characterized by probability density *p(x*), deviation is calculated by the formula

where

The following theorem has great significance in the theory of probability: the deviation of the sum of independent terms is equal to the sum of their deviations. No less important is Chebyshev’s inequality, which allows us to evaluate the probability of large deviations of the random variable *X* from its expected value.

### REFERENCE

Gnedenko, B. V.*Kurs teorii veroiatnostei*, 5th ed. Moscow, 1969.

## deviation

**i**. The angular difference between a magnetic and a compass heading. It is a compass error caused by the compass magnet attempting to align with the aircraft's local magnetic field. The deviation error changes with the aircraft heading and the latitude. It is measured in degrees east (+) or west (−), depending on whether the north-seeking end of the compass needle lies to the east or west of magnetic north.

**ii**. The angle between the wind and the pressure gradient.

**iii**. In frequency modulation, the amount the carrier increases or decreases when modulated.

**vi**A departure from a current clearance, such as an off-course maneuver, to avoid bad weather or turbulence.

**v**A variation from set rules and regulations. Where specifically authorized in the regulation and requested by the pilot, ATC (air traffic control) may permit pilots to deviate from certain regulations.

**vi**. In flight, a sudden excursion from the normal flight path.

**vii**. The distance by which a weapon misses its target.