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• minimum: X_min = min(X₁, X₂, X₃, ..., X_N )
• maximum: X_max = max(X₁, X₂, X₃, ..., X_N )
• arithmetic mean:
• median: middle value of the ranked series X_i
• mode: value of X which occurs with the greatest frequency; i.e. the middle value of the class with the greatest frequency. If classes have equal greatest frequency then the middle value of the class with the lowest class levels will be indicated as mode.
• standard deviation:
• variance = σx*σx
• skewness:
• kurtosis:
• quantiles and deciles:
  •  the quantiles and deciles are computed with the function:
    
    where k = the rank in sorted data array.
    If k is not an integer X{~}k~ _k is interpolated between the two closest values
• empirical frequency distribution: graphical presentation of number of data per class; number of classes and minimum and maximum class levels are input
• empirical cumulative frequency distribution: cumulative representation of frequencies per class. The relative cumulative frequencies are computed by:
   

As can be seen, the relative cumulative frequency is plotted with the Chegodayev function
For the mean and the variance also the 95% confidence intervals will be computed. The Student-t distribution is to be applied and the percentage points t_{n,α /2} and t_{n,1-α /2} . are computed, where n = N - 1 is the number of degrees of freedom. The confidence limits for the mean then read:

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Given an estimate of the sample variance the true variance s{~}Y~ σY² will be contained within the following confidence interval with a probability of 100(1-α) %:

The values for cχ²_n,α/2 and c2^ χ2_n,1-α/2 are read from the tables of the Chi-square distribution for given aand n.

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