# NORMAL DISTRIBUTION

A mathematical law which predicts the probability that the random error of any given observation of a series of observations of a certain quantity will lie within certain bounds. The law can be derived from the following properties of random errors: (1) positive and negative errors of the same magnitude are about equal in number, (2) small errors occur more frequently than large errors, and (3) extremely large errors rarely occur. One immediate consequence of these properties is that the average or mean value of a large number of observations of a given quantity is zero. Also called GAUSSIAN DISTRIBUTION.

## Related Terms

### CRITICAL OPERATION

Operations where an error may immediately cause an accident or a situation that could threaten lives, the environment or the ship.

### KALMAN FILTER

A linear system in which the mean squared error between the desired output and the actual output is minimized when the input is a random signal generated by white noise.

### INTEGRAL SQUARE ERROR

A measure of system performance formed by integrating the square of the system error over a fixed interval of time; this performance measure and its generalizations are frequently used in linear optimal control and estimation theory.

### INTEGRAL-MODE CONTROLLER

A controller which produces a control signal proportional to the integral of the error signal.

### HODGSON NUMBER

Method of predicting the metering error during pulsating gas flow when a surge tank is located between the pulsation source (pump or compressor) and the meter (orifice, nozzle, or venturi).

### GYRO ERROR

The error in the reading of the gyrocompass, expressed in degrees east or west to indicate the direction in which the axis of the compass is offset from true north.

### HALVING

The process of adjusting magnetic compass correctors so as to remove half of the deviation on the opposite cardinal or adjacent intercardinal headings to those on which adjustment was originally made when all deviation was removed. This is done to equalize the error on opposite headings.

### HYSTERESIS ERROR

That error in the reading of an instrument due to hysteresis

### INDEX CORRECTION

The correction due to index error

### EFFECTIVE RANGE

The range of values of the measured quantity for which any single measurement, obtained under specified conditions of use of a measuring instrument, should not be in error by more than a specified amount. NOTE: The effective range may be the whole or a specified part of the interval between the lower and upper range limits. Also known as measuring range, working range

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