measures of variation

'measures of variation' can also refer to...

measures of variation

measures of variation

Clustering methods based on variational analysis in the space of measures

Measuring variation in the frequency of group fission and fusion from continuous monitoring of group sizes

Copy number variation has little impact on bead-array-based measures of DNA methylation

Comparison of microfluidic digital PCR and conventional quantitative PCR for measuring copy number variation

Measuring the cold dark matter power spectrum from variations of Hubble flows

Albumin as an outcome measure in haemodialysis in patients: the effect of variation in assay method

Molecular line intensities as measures of cloud masses – I. Sensitivity of CO emissions to physical parameter variations

Validation of the nucleotide excision repair comet assay on cryopreserved PBMCs to measure inter-individual variation in DNA repair capacity

Correlations among measures of phenotypic and genetic variation within an oligotrophic asexual yeast, Candida sonorensis, collected from Opuntia

Application of a Repeat-Measure Biomarker Measurement Error Model to 2 Validation Studies: Examination of the Effect of Within-Person Variation in Biomarker Measurements

Corrigendum to: “Correlations among measures of phenotypic and genetic variation within an oligotrophic asexual yeast, Candida sonorensis, collected from Opuntia” [FEMS Yeast Research 4 (2004) 527–540]

Need for a consensus on the methods by which to measure joint mobility and the definition of norms for hypermobility that reflect age, gender and ethnic-dependent variation: is revision of criteria for joint hypermobility syndrome and Ehlers–Danlos syndrome hypermobility type indicated?


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Quantities that express the amount of variation in a random variable (compare measures of location). Variation is sometimes described as spread or dispersion to distinguish it from systematic trends or differences. Measures of variation are either properties of a probability distribution or sample estimates of them.

The range of a sample is the difference between the largest and smallest value. The interquartile range is potentially more useful. If the sample is ranked in ascending order of magnitude two values of x may be found, the first of which is exceeded by 75% of the sample, the second by 25%; their difference is the interquartile range. An analogous definition applies to a probability distribution.

The variance is the expectation (or mean) of the square of the difference between a random variable and its mean; it is of fundamental importance in statistical analysis. The variance of a continuous distribution with mean μ is ∫(x − μ)2f(x) dx and is denoted by σ2. The variance of a discrete distribution is ∑ (x − μ)2p(x) and is also denoted by σ2. The sample variance of a sample of n observations with mean is ∑ (xi)2 / (n − 1) and is denoted by s2. The value (n − 1) corrects for bias.

∫(x − μ)2f(x) dx

∑ (x − μ)2p(x)

∑ (xi)2 / (n − 1)

The standard deviation is the square root of the variance, denoted by σ (for a distribution) or s (for a sample). The standard deviation has the same units of measurement as the mean, and for a normal distribution about 5% of the distribution lies beyond about two standard deviations each side of the mean. The standard deviation of the distribution of an estimated quantity is termed the standard error.

The mean deviation is the mean of the absolute deviations of the random variable from the mean.

Subjects: Computing.

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