(statistics) The ratio of the standard deviation of a distribution to its arithmetic mean.
Coefficient of variation
| Sci-Tech Dictionary: coefficient of variation |
(¦kō·ə′fish·ənt əv ′ver·ē′ā·shən)
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| Investment Dictionary: 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 to another, even if the means are drastically different from each other.
Investopedia Says:
In the investing world, the coefficient of variation allows you to determine how much volatility (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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| Accounting Dictionary: Coefficient of Variation |
Measure of relative dispersion, or relative risk. It is computed by dividing the standard deviation (s) by the expected value (x-). For example, consider two investment proposals, A and B, with the following data:
Therefore, because the coefficient is a relative measure of risk, B is considered more risky than A.
| Geography Dictionary: coefficient of variation |
V
The standard deviation of a data set expressed as a percentage of the arithmetic mean, this is a measurement of the amount of variation in a data set. The lower the value of V, the more the overall data approximate to the mean. It is used in comparing two apparently similar data sets.
| Architecture: coefficient of variation |
The standard deviation expressed as a percentage of the average.
| Wikipedia: Coefficient of variation |
In probability theory and statistics, the coefficient of variation (CV) is a normalized measure of dispersion of a probability distribution. It is defined as the ratio of the standard deviation 
to the mean 
:
This is only defined for non-zero mean, and is most useful for variables that are always positive. It is also known as unitized risk.
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. However the mean temperature of the data set would be different in each scale and thus the coefficient of variation would be different. So the coefficient of variation does not have any meaning for data on an interval scale.[1]
Standardized moments are similar ratios, 
, which are also dimensionless and scale invariant. The variance-to-mean ratio, σ2 / μ, is another similar ratio, but is not dimensionless, and hence not scale invariant.
See Normalization (statistics) for further ratios.
In signal processing, particularly image processing, the reciprocal ratio μ / σ is referred to as the signal to noise ratio.
Contents |
Comparison to standard deviation
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 a dimensionless 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.
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 construct confidence intervals for the mean.
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 the normal distribution. The standard deviation of an exponential distribution is equal to its mean, so its coefficient of variation is equal to 1. Distributions with CV < 1 (such as an Erlang distribution) are considered low-variance, while those 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 variation of the CV is the CV(RMSD). Essentially the CV(RMSD) replaces the standard deviation term with the Root Mean Square Deviation (RMSD).
See also
Similar ratios
- Standardized moment, μk / σk
- Variance-to-mean ratio, σ2 / μ
- Fano factor,
(windowed VMR) - Signal to noise ratio, μ / σ (in signal processing)
External links
References
- ^ "What is the difference between ordinal, interval and ratio variables? Why should I care?". GraphPad Software Inc. http://www.graphpad.com/faq/viewfaq.cfm?faq=1089. Retrieved on 2008-02-22.
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