WebCab Probability and Statistics for .NET v3.3 Demo

BasicStatistics.ChebyshevTheorem Method 

Calculates the percentage of items that must be within a specified number of standard deviations from the mean.

public double ChebyshevTheorem(
   double noStandDev
);

Parameters

noStandDev
The number of standard deviations from the mean. Note that the number of standard deviation could be a non-integer but has too be greater than one.

Remarks

Note that, before this methods is called a data set should be registered by invoking the method SetDataSet. This method is a direct application of Chebyshev's Theorem which states the following:

Chebyshev's Theorem: At least (1-1/z2) of the items in any data set must lie within z standard deviations of the mean of the same data set when z is any real number greater than 1.

Example: If we take noStandDev = 2, then this method returns the proportion of the data set which lies within the interval [m - (2 * SD), m +(2 * SD)], where m is the mean of the data set considered and SD is the standard deviation of the data set considered. Note that if A is the proportion returned then the corresponding percentage of items within the interval is (A * 100).

Exceptions

Exception TypeCondition
StatisticsExceptionThrown if no data set has been registered for the present instance of the class.

See Also

BasicStatistics Class | WebCab.Libraries.Statistics.Statistics Namespace