# Deviation

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Related to Deviation: standard deviation, Average deviation

## deviation

[‚dēv·ē′ā·shən]
(engineering)
The difference between the actual value of a controlled variable and the desired value corresponding to the set point.
(evolution)
Evolutionary differentiation involving interpolation of new stages in the ancestral pattern of morphogenesis.
(optics)
The angle between the incident ray on an object or optical system and the emergent ray, following reflection, refraction, or diffraction. Also known as angle of deviation.
(petroleum engineering)
During a drilling operation, the inclination of the borehole from the vertical.
(statistics)
The difference between any given number in a set and the mean average of those numbers.

## 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 - mx)2 of the square of the deviation of X from its expected value mx =E(X). The deviation of a random variable X is denoted by D(X) or by σ2). The square root of the deviation (that is, if the deviation is σ2) 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.
References in classic literature ?
We left Zanzibar at nine o'clock in the morning," said the doctor, consulting his notes, "and, after two days' passage, we have, including our deviations, travelled nearly five hundred geographical miles.
One can distinguish on its ruins three sorts of lesions, all three of which cut into it at different depths; first, time, which has insensibly notched its surface here and there, and gnawed it everywhere; next, political and religious revolution, which, blind and wrathful by nature, have flung themselves tumultuously upon it, torn its rich garment of carving and sculpture, burst its rose windows, broken its necklace of arabesques and tiny figures, torn out its statues, sometimes because of their mitres, sometimes because of their crowns; lastly, fashions, even more grotesque and foolish, which, since the anarchical and splendid deviations of the Renaissance, have followed each other in the necessary decadence of architecture.
The staircase was as wooden and solid as need be, and Affery went straight down it without any of those deviations peculiar to dreams.
They allowed for some human intermediation in language processing of the problem text, but the AI program alone automatically solved the problems, scoring a deviation value of 64.
Standard deviation estimates the variability in the population from which the study sample was drawn, and standard error is a measure of how precise the sample mean is.
The Banca d'Italia has proposed a deviation from the Basel III rules for banks in the country.
Physicians at the hospital said that attention deficit disorder is one of the most commonly associated symptoms of nasal septum deviation.
Physicians at the University Hospital Sharjah said that Attention Deficit Disorder (ADD) is one of the most common of the associated symptoms of nasal septum deviation.
The firm analyzed each term of the five presidents who have held the office since 1980 and rated them by the standard deviation in their approval ratings, which refers to how clustered a certain set of data is; the lower the standard deviation, the more clustered.
To fully understand the effect of aperture shape on volume, however, standard deviation must be analyzed.
For instance, the 2000 congressional redistricting plan in Pennsylvania had a deviation of just nineteen people, but the people that drew the plan had no compelling explanation for why these deviations existed.
Arithmetic corrections, price adjustments against guaranteed efficiencies of turbines and generators and other technical, commercial deviations were accounted for.

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