Glossar

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E

Errors

Systematic Errors
Systematic errors are caused by the measuring apparatus itself. The measurement result is distorted in the same direction every time the measurement is taken. Causes can be, for example, incorrect calibration of the measuring instruments, incorrect measuring set-ups or failure to take account of external influences such as voltage, temperature or air pressure fluctuations. The limited accuracy of measuring instruments must also be considered a systematic error. Such errors can only be detected and avoided by great care and experience of the experimenting person.

Statistical Errors
When measuring one and the same physical quantity, the same values do not result in the same values for each measurement. They fluctuate or scatter around a mean value. Unlike the systematic errors, the statistical errors do not always falsify the measurement result in the same direction. They are caused, for example, by inaccurate reading from the measuring instrument, by vibrations of the measuring instrument or by fluctuations of the quantity to be measured itself. Such errors can only be determined and corrected by mathematical methods.

For more detailed information see the definition and description of Wolfram Experimental Data Analyst Documentation.

Exponential Functions

Exponential functions are mainly used to model percentage increases or decreases, multiplication times or half-lives. The general form is

$f\left(x\right)=a\cdot bx$

The parameter $a$ influences the slope and curvature of the graph and specifies the point of intersection with the y-axis (if the graph has not been moved along the x- and y-axis).
For $\mathrm{b > 1}$ the curve is monotonically rising, for $\mathrm{0 < b < 1}$ monotonically falling.

A special case is the natural or e-function $ex$, which is also displayed as  exp(x) .