Functions for descriptive statistics

Descriptive statistics aim at characterising empirical data by summative parameters (and also by tables and plots}.

Standard functions defined in math unit

The unit math of the RTL provides a plethora of routines for descriptive statistics.

• mean: Returns the mean value of an array.
• stddev: Returns the (sample) standard deviation of an array.
• popnstddev: Returns the (population) standard deviation of an array.
• meanandstddev: Returns mean and standard deviation of an array.
• momentskewkurtosis: Returns the first four moments of an array.
• variance: Returns the (sample) variance of an array.
• popnvariance: Returns the (population) variance of an array.
• totalvariance: Returns the total variance of an array.
• sumofsquares: Returns the sum of squares of an array.
• sum: Returns the sum of values of an array.
• sumsandsquares: Returns sum and sum of squares of the values in an array.

These functions expect an array of predefined length (e.g. array[1..100] of float) or a 0-based open array (e.g. array of extended) with subsequent call of the SetLength procedure.

Standard functions defined in other units

• length: Delivers the length (n) of an array.

Custom functions

Standard error of the mean

The standard error of the mean (SEM) is a measure that estimates how precisely the true mean of the population can be known.

Calculation of SEM is simple:

  function sem(const data: array of Extended): real;
  begin
    sem := stddev(data) / sqrt(length(data));
  end;