Coefficient of Variation CV: Definition, Formula & Example

The nonproportionality between the mean and the standard deviation is not problematic if one’s goal is to quantify or predict variation. However, further interpretation of such a difference in evolvability should consider the possibility that this difference results from a nonproportional relationship between the mean and the standard deviation. Understanding the causes for such nonproportionality may become critical for interpreting differences in variation among quantitative traits. Below, we present some of the most common causes for nonproportionality between the mean and the standard deviation and we discuss the consequences of these when comparing variation. 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.

Intro to Statistics

For example, investors or analysts might want to find an asset that has a low degree of volatility in its history. And this is relative to the return and is also in relation to the rest of the industry or overall market. For example, it can show or help determine the amount of risk or volatility compared to the expected amount of return from an investment. In most cases, if the coefficient of variation formula indicates a lower ratio of the standard deviation to mean return, then the trade-off between risk and return can be better.

1. When the mean value is close to zero, the CV becomes very sensitive to small changes in the mean.
2. We also demonstrate how this relationship can be used to address practical problems in a clinical laboratory.
3. If you work with data, you may have encountered the coefficient of variation (CV) as a measure of relative variability.
4. The choice of k may also be made to optimize the sensitivity and specificity of diagnostic tests by employing k as a cutoff.
5. Coefficient of Variation (CV) is a standardized measure of the dispersion of a probability distribution or frequency distribution.

How Do I Calculate the Coefficient of Variation?

If you want to compare the variation in prices in the U.S. grocery store and the Japanese store, you cannot simply compare standard deviations since they are measured in different units—yen and U.S. dollars. For example, if you have data for temperatures measured in Fahrenheit, both the mean and standard deviation of the data will be measured in Fahrenheit. No set value can be considered universally “good.” However, generally speaking, it is often the case that a lower coefficient of variation is more desirable, as that would suggest a lower spread of data values relative to the mean. If the expected return in the denominator of the coefficient of variation formula is negative or zero, then the result could be misleading. When we are presented with estimated values, the CV relates the standard deviation of the estimate to the value of this estimate. The lower the value of the coefficient of variation, the more precise the estimate.

Wood’s formulation was a valuable link between the precision of titration assays and an operational assessment of assay performance. Reaction norms for one trait, plant height, measured for two genotypes (red and blue) in two different environmental gradients, temperature on the left and soil moisture on the right. In the two experiments, plasticity is measured for each genotype as the difference in phenotypic value divided by the change in either temperature or moisture. Thus, on the left phenotypic plasticity is expressed as cm °C−1, whereas on the right it is expressed as cm% humidity−1.

How can you interpret the CV in data analysis?

Meaningful comparison of variation in quantitative trait requires controlling for both the dimension of the varying entity and the dimension of the factor generating variation. Although the coefficient of variation (CV; standard deviation divided by the mean) is often used to measure and compare variation of quantitative traits, it only accounts for the dimension of the former, and its use for comparing variation may sometimes be inappropriate. Here, we discuss the use of the CV to compare measures of evolvability and phenotypic plasticity, two variational properties of quantitative traits. Using a dimensional analysis, we show that contrary to evolvability, phenotypic plasticity cannot be meaningfully compared across traits and environments by mean‐scaling trait variation.

So it is ok to compute a CV for variables such as weight, time, distance, enzyme activity… But it is not ok to compute the CV for variab3es such as temperature (in C or F) or pH. For these variables, the zero point is arbitrary. If you did, you’d get a different CV, which makes the CV no longer a sensible way to quantify variation. A high Coefficient of Variation indicates high variability relative to the mean, suggesting that the data points are spread out over a wide range of values. Conversely, a low CV indicates low variability relative to the mean, suggesting that the data points are closely clustered around the mean.

Phenotypic plasticity and evolvability are two aspects of the variation of quantitative traits. Phenotypic plasticity corresponds to the variation expressed by a genotype when exposed to different environments (Bradshaw 1965; Schlichting 1986; DeWitt and Scheiner 2004), and evolvability (sensu Houle 1992) is the ability of a trait to respond to selection. Various measurements have been developed to quantify phenotypic variation produced by a given change in the environment or a given strength of selection. Advanced statistical models to handle increasingly large and complex datasets are often employed at the expense of attention given to the meaning of the numbers (Houle et al. 2011; Tarka et al. 2015). This issue affects several aspects of the scientific process, from the measurement procedures to the interpretation of the statistical analyses where biological significance is often confounded with statistical significance (Yoccoz 1991; Tarka et al. 2015; Wasserstein and Lazar 2016).

We further emphasize the need of remaining cognizant of the dimensions of the traits and the relationship between mean and standard deviation when comparing CVs, even when the scales on which traits are expressed allow meaningful calculation of the CV. The problems exposed here are common in the literature in ecology and evolution where using the CV as a dimensionless measure of variation is widespread. Notice that variance‐standardization (e.g., Z‐transformation, heritability, and selection intensity) is often subject to similar shortcoming when it comes to compare variation (Hereford et al. 2004; Hansen et al. 2011; Houle et al. 2011; Matsumura et al. 2012). More generally, standardization and transformation of data are routinely performed before data analyses without paying attention to the consequences of these manipulations on the meaning of the numbers.

1. If you find a coefficient of variation of 0.10 or 10%, the standard deviation is one-tenth or 10% of the mean.
2. On the other hand, if you have a CV of 50%, it means that the standard deviation is 50% of the mean.
3. The good news is that calculating the coefficient of variation can be a fairly simple process as long as you have the relevant information.
4. The CV for a variable can easily be calculated using the information from a typical variable summary (and sometimes the CV will be returned by default in the variable summary).

To minimize these common mistakes, we advocate a stronger emphasis on the meaning of the numbers when teaching quantitative methods. Although assay variability is well recognized as pertinent to the interpretation of quantitative bioassays such as the enzyme-linked immunosorbent assay (ELISA), few tools that link assay precision with interpretation of results are readily available. In our investigations, we have expanded on previous studies that evaluated the relationship between assay precision and the capabilities and limitations of a given assay system.

On the flip side, an investor that’s more risk-seeking might want to find and invest in an asset that has previously had a high degree of volatility. However, with that said, it’s always important to recognize that if the expected return ends up being zero or a negative number, it might not be fully accurate and could be misleading. Standard deviation is one of the most crucial concepts in the field of Statistics. Here, we’ll take you through its definition and uses, and then teach you step by step how to calculate it for any data set. The data on the left shows how the price of a carton of milk varied in a U.S. grocery store over the course of a year. The data on the right shows how the price of a carton of milk varied in a Japanese grocery store over the course of a year.

There are also some disadvantages worth understanding for the coefficient of variation to be interpreted the way it’s supposed to be. It’s an effective statistical measure that can help protect an investor from a potentially volatile investment. As well, it can help predict investment returns by considering account data from several different periods. This article is a guide on sample standard deviation, including concepts, a step-by-step process to calculate it, and a list of examples. Based on the approximate figures, the investor could invest in either the SPDR S&P 500 ETF or the iShares Russell 2000 ETF, since the risk/reward ratios are approximately the same and indicate a better risk-return tradeoff than the Invesco QQQ ETF.

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This can be related to uniformity of velocity profile, temperature distribution, gas species (such as ammonia for an SCR, or activated carbon injection for mercury absorption), and other flow-related parameters. The Percent RMS also is used to assess flow uniformity in combustion systems, HVAC systems, ductwork, inlets to fans and filters, air handling units, etc. where performance of the equipment is influenced by the incoming flow distribution. If the number of observed pairs equals or exceeds the table value, the null hypothesis that the CV is at most the indicated value is rejected. No, the CV cannot be negative because both the standard deviation and the mean are always non-negative. Notice that IA represents an elasticity, that is, a proportional change in the trait per proportional change in fitness (van Tienderen 2000; Caswell 2001; Hansen et al. 2003, 2011). The coefficient of variation is used coefficient of variation meaning in many different fields, including chemistry, engineering, physics, economics, and neuroscience.