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Coefficient Of Variation - CV

A statistical measure of the dispersion of data points in a data series around the mean. It

is calculated as follows:

The coefficient of variation represents the ratio of the standard deviation to the mean, and

it is a useful statistic for comparing the degree of variation from one data series toanother, even if the means are drastically different from each other.

Coefficient of variation

Inprobability theory and statistics, the coefficient of variation (CV) is anormalized measure

ofdispersion of a probability distribution. It is defined as the ratio of thestandard deviation to

the mean :

This is only defined fornon-zero mean, and is most useful for variables that are alwayspositive.

It is also known as unitized risk or thevariation coefficient. It is expressed as percentage.

The coefficient of variation should only be computed for data measured on a ratio scale. As an

example, if a group of temperatures are analyzed, the standard deviation does not depend on

whether the Kelvin or Celsius scale is used since an object that changes its temperature by 1 K

also changes its temperature by 1 C. However the mean temperature of the data set would differ

in each scale by an amount of 273 and thus the coefficient of variation would differ. So the

coefficient of variation does not have any meaning for data on aninterval scale.[1]

Standardized moments are similar ratios, , which are also dimensionless and scale invariant.

The variance-to-mean ratio, 2 / , is another similar ratio, but is not dimensionless, and hence

not scale invariant.

SeeNormalization (statistics) for further ratios.

Insignal processing, particularly image processing, thereciprocal ratio / is referred to as

the signal to noise ratio.

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Contents

[hide]

1 Comparison to standard deviation

o

1.1 Advantages

o 1.2 Disadvantages

2 Applications

3 Distribution

4 See also

o 4.1 Similar ratios

5 External links

6 References

[edit]Comparison to standard deviation

[edit]Advantages

The coefficient of variation is useful because the standard deviation of data must always be

understood in the context of the mean of the data. The coefficient of variation is adimensionless

number. So when comparing between data sets with different units or widely different means,

one should use the coefficient of variation for comparison instead of the standard deviation.

[edit]Disadvantages

When the mean value is near zero, the coefficient of variation is sensitive to small

changes in the mean, limiting its usefulness.

Unlike the standard deviation, it cannot be used to constructconfidence intervals for

the mean.

[edit]Applications

The coefficient of variation is also common in applied probability fields such as renewal

theory,queueing theory, and reliability theory. In these fields, the exponential distribution is often

more important than thenormal distribution. The standard deviation of anexponential

distribution is equal to its mean, so its coefficient of variation is equal to 1. Distributions with CV 1 (such as

a hyper-exponential distribution) are considered high-variance. Some formulas in these fields are

expressed using the squared coefficient of variation, often abbreviated SCV. In modeling, a

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variation of the CV is the CV(RMSD). Essentially the CV(RMSD) replaces the standard deviation

term with the Root Mean Square Deviation (RMSD).

[edit]Distribution

Under weak conditions on the sample distribution, the probability distribution of the coefficient of

variation is known. In fact, it has been determined by Hendricks and Robey[2]. This is useful, for

instance, in the construction ofhypothesis tests orconfidence intervals.

[edit]See also

Normalization (statistics)

[edit]Similar ratios

Standardized moment, k / k

Variance-to-mean ratio, 2 /

Fano factor, (windowed VMR)

Signal to noise ratio, / (in signal processing)

Signal to noise ratio (image processing)

[edit]External links

Geometric Coefficient of Variation

[edit]References

1.^ "What is the difference between ordinal, interval and ratio variables? Why should I

care?". GraphPad Software Inc. Retrieved 2008-02-22.

2.^ The Sampling Distribution of the Coefficient of Variation, Walter A. Hendricks and Kate

W. Robey, Ann. Math. Statist. Volume 7, Number 3 (1936), 129-132.

[hide]vde

Statistics

[hide]

Descriptive statistics

Continuous data LocationMean (Arithmetic,Geometric,Harmonic) MedianMode

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DispersionRange Standard deviation Coefficient of variation Percentile Interquartile range

ShapeVarianceSkewnessKurtosisMoments L-moments

Count dataIndex of dispersion

Summary tablesGrouped data Frequency distribution Contingency table

Statistical graphicsBar chartBiplot Box plot Control chartCorrelogramForest plotHistogram Q-Q plotRun chartS

Explanation OfCoefficient Of Variation - CV

In the investing world, the coefficient of variation allows you to determine how muchvolatility (risk) you are assuming in comparison to the amount of return you can expect

from your investment. In simple language, the lower the ratio of standard deviation to

mean return, the better your risk-return tradeoff.

Note that if the expected return in the denominator of the calculation is negative or zero,

the ratio will not make sense.

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