Category Archives: Statistik

Outlier

An outlier is an observation that lies outside the overall pattern of a distribution (Moore and McCabe 1999). Usually, the presence of an outlier indicates some sort of problem. This can be a case which does not fit the model … Continue reading

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Variation Coefficient

If is the standard deviation of a set of samples and its mean, then CITE THIS AS: Weisstein, Eric W. “Variation Coefficient.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/VariationCoefficient.html

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Mean Deviation

The mean deviation (also called the mean absolute deviation) is the mean of the absolute deviations of a set of data about the data’s mean. For a sample size , the mean deviation is defined by (1) where is the … Continue reading

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Standard Deviation

The standard deviation of a probability distribution is defined as the square root of the variance , <img src="http://mathworld.wolfram.com/images/equations/StandardDeviation/Inline5.gif" alt="sqrt(-^2)” width=”79″ height=”26″ border=”0″ /> (1) (2) where <img src="http://mathworld.wolfram.com/images/equations/StandardDeviation/Inline9.gif" alt="mu=x^_=” width=”69″ height=”14″ border=”0″ /> is the mean, <img src="http://mathworld.wolfram.com/images/equations/StandardDeviation/Inline10.gif" alt="mu_2^'=” … Continue reading

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Weighted Mean

The weighted mean of a discrete set of numbers with weights is given by <img src="http://mathworld.wolfram.com/images/equations/WeightedMean/NumberedEquation1.gif" alt=" =sum_(i=1)^nw_ix_i, ” width=”84″ height=”46″ border=”0″ /> (1) where each weight is a nonnegative real number and (2) For a continuous set of numbers … Continue reading

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Geometric Mean

The geometric mean of a sequence is defined by (1) Thus, (2) (3) and so on. The geometric mean of a list of numbers may be computed using GeometricMean[list] in the Mathematica package DescriptiveStatistics` . For , the geometric mean … Continue reading

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Arithmetic Mean

The arithmetic mean of a set of values is the quantity commonly called “the” mean or the average. Given a set of samples , the arithmetic mean is (1) It can be computed in Mathematica using Mean[list]. The arithmetic mean … Continue reading

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Measures of Position

Statisticians often talk about the position of a value, relative to other values in a set of observations. The most common measures of position are quartiles, percentiles, and standard scores (aka, z-scores). Percentiles Assume that the elements in a data … Continue reading

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Statistics Formulas

Parameters Population mean = μ = ( Σ Xi ) / N Population standard deviation = σ = sqrt [ Σ ( Xi - μ )2 / N ] Population variance = σ2 = Σ ( Xi – μ )2 … Continue reading

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Chi-Square Goodness-of-Fit Test

This lesson explains how to conduct a chi-square goodness of fit test. The test is applied when you have one categorical variable from a single population. It is used to determine whether sample data are consistent with a hypothesized distribution. … Continue reading

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