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This algorithm can easily be adapted to compute the variance of a finite population: simply divide by n instead of n − 1 on the last line.. Because SumSq and (Sum×Sum)/n can be very similar numbers, cancellation can lead to the precision of the result to be much less than the inherent precision of the floating-point arithmetic used to perform the computation.
Perl 5 hashes are flat: keys are strings and values are scalars. However, values may be references to arrays or other hashes, and the standard Perl 5 module Tie::RefHash enables hashes to be used with reference keys. A hash variable is marked by a % sigil, to distinguish it from scalar, array
Given any list as an input: Count the number of elements. Given a list of numbers: Find the k largest or smallest elements, k given in advance. Find the sum, mean, variance and standard deviation of the elements of the list. See also Algorithms for calculating variance. Given a list of symbols from an alphabet of k symbols, given in advance.
modified_identifier_list «As «non_array_type««array_rank_specifier»» (multiple declarator); valid declaration statements are of the form Dim declarator_list , where, for the purpose of semantic analysis, to convert the declarator_list to a list of only single declarators:
The use of n − 1 instead of n in the formula for the sample variance is known as Bessel's correction, which corrects the bias in the estimation of the population variance, and some, but not all of the bias in the estimation of the population standard deviation. It is not possible to find an estimate of the standard deviation which is unbiased ...
Given a random variable X ~ Norm[μ,σ] (a normal distribution with mean μ and standard deviation σ) and a constant L > μ, it can be shown via integration by substitution: [] = + (()) where A and B are certain numeric constants.
Python supports a wide variety of string operations. Strings in Python are immutable, so a string operation such as a substitution of characters, that in other programming languages might alter the string in place, returns a new string in Python. Performance considerations sometimes push for using special techniques in programs that modify ...
The mean and the standard deviation of a set of data are descriptive statistics usually reported together. In a certain sense, the standard deviation is a "natural" measure of statistical dispersion if the center of the data is measured about the mean. This is because the standard deviation from the mean is smaller than from any other point.