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How to Interpret the Coefficient of Variation in Data Analysis

In a similar fashion, p(k) is the same regardless of the base of the logarithm by which the original values are transformed; equation A4, which uses the natural logarithm, is universally applicable. Thus, if other statistical analysis requires a logarithm, chosen for convenience or even arbitrarily, other than the natural logarithm, p(k) is unaffected and always calculated the same way. This property of invariance contrasts with the probabilistic interpretation of the SD, which differs with choice of logarithm base. Second, although equation A4 is predicated on the assumption that assay values are lognormally distributed, the CV is the ratio of the SD to the mean of the original values, and correspondingly p(k) refers to ratios of the original values.

Measurements that are log-normally distributed exhibit stationary CV; in contrast, SD varies depending upon the expected value of measurements. The coefficient of variation (CV) indicates the size of a standard deviation in relation to its mean. The higher the coefficient of variation, the greater the dispersion level around the mean. Other than helping when using the risk/reward ratio to select investments, it is used by economists to measure economic inequality.

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). Alternatively, p(k) for k values of 1.5, 2, 3, and 4 may be obtained from the nomogram of Fig. In this article, we have covered the Coefficient of Variation Definition, its related formulas, examples and others in detail. This section collects any data citations, data availability statements, or supplementary materials included in this article. They’re most often used to analyze dispersion around the mean, but quartile, quintile, or decile CVs can also be used to understand variation around coefficient of variation meaning the median or 10th percentile, for example. Adam Hayes, Ph.D., CFA, is a financial writer with 15+ years Wall Street experience as a derivatives trader.

Coefficient of Variation (CV): Definition, Formula & Example

Because this quantity is not dimensionless, it cannot be compared meaningfully when plasticity is measured across different environmental gradients (Fig. 1). Still, variance measures the dispersion of data in squared units that are hard to interpret. In contrast, the standard deviation converts variance into “standardized,” easy-to-interpret units that are the same as the units used in your data. The CV can help you answer questions about how variable your data are relative to the mean. For example, if you have a CV of 10%, it means that the standard deviation is 10% of the mean. This indicates a low variability, as most of the data are close to the mean.

Comparison to standard deviation

The CV is useful for comparing the variability of data sets that have different units or scales. For example, if you want to compare the variability of the heights of students in different classes, you cannot use the standard deviation alone, because it depends on the units of measurement (e.g., centimeters or inches). The CV, however, is unitless and expresses the variability as a percentage of the mean. This way, you can see which class has more or less variation in heights, regardless of the units. Several studies comparing phenotypic plasticity have acknowledged this issue. In contrast, comparing mean standardized phenotypic plasticity of traits measured along different environmental gradients (among experiment comparison in Fig. 1; e.g., Murren et al. 2014; Acasuso‐Rivero et al. 2019) is meaningless.

1. 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.
2. For example, you cannot use the CV to compare the variability of temperatures in Celsius or Fahrenheit, because they are not based on a true zero point and can have negative values.
3. It enables us to supply relatively simple and quick tools that help us to compare the data of different series.
4. 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.
5. Thus, dividing a measure of plasticity by the trait mean provides a measure of trait variation proportional to the trait mean per unit change of the environmental factor.

As well, the investor is able to assume that each ETF has roughly the same returns compared to their long-term averages. Let’s say that a risk-averse investor is looking into an exchange-traded fund (ETF) as an investment. An ETF is essentially several securities that are able to track a market index broadly. On the other hand, a lower standard deviation shows that the values are likely to be grouped around the mean.

Standard Deviation

If, for example, the data sets are temperature readings from two different sensors (a Celsius sensor and a Fahrenheit sensor) and you want to know which sensor is better by picking the one with the least variance, then you will be misled if you use CV. The problem here is that you have divided by a relative value rather than an absolute. The coefficient of variation is a simple way to compare the degree of variation from one data series to another. It can be applied to pretty much anything, including the process of picking suitable investments.

You could convert the Japanese prices into dollars, but that would be more work than simply calculating the coefficient of variation. When we compare the coefficient of variation for two data sets, we see that the coefficient of 0.08 is much smaller than the coefficient of variation for the U.S. data, 0.72. This tells you that the prices varied more in the U.S. grocery store than in the Japanese grocery store. The coefficient of variation (CV)—also called the relative standard deviation (RSD)—is the ratio of the standard deviation to the mean. It is a parameter or statistic used to convey the variability of your data in relation to its mean. The sample standard deviations are still 15.81 and 28.46, respectively, because the standard deviation is not affected by a constant offset.

Chapter 8: Measures of Dispersion

In plain language, it is meaningful to say that 20 Kelvin is twice as hot as 10 Kelvin, but only in this scale with a true absolute zero. While a standard deviation (SD) can be measured in Kelvin, Celsius, or Fahrenheit, the value computed is only applicable to that scale. Only the Kelvin scale can be used to compute a valid coefficient of variability.

In finance, the coefficient of variation allows investors to determine how much volatility, or risk, is assumed in comparison to the amount of return expected from investments. Ideally, if the coefficient of variation formula should result in a lower ratio of the standard deviation to mean return, then the better the risk-return tradeoff. The CV is never exactly known and must be estimated from appropriate validation studies. Such studies will typically provide a range of estimates of intra-assay, interassay, and combined variability on serum samples which cover the working range of analyte concentrations. The following should be kept in mind in determining the value of CV to use in equation A4. (ii) The values anticipated for the test samples may influence which CV to use, because, even though the CV is for the most part independent of the mean value, values toward the extremes of the working range tend to display higher CVs.

As expressed above, in the context of serum assays and other applications the CV may be preferred over SD as a measure of precision, but there is no published formulation that links the CV to assay performance in a manner analogous to Wood’s treatment of the SD in the log scale. Such a formulation would be even more useful if it were to generalize from twofold to k-fold disparities in replicate measurements (where k can be any number greater than one and arbitrarily close to one). This generalization would take advantage of the fact that ELISAs and other assays with continuous scales are capable of measuring a continuous range of differences in samples, unlike classic titration assays utilizing step-wise, usually twofold, serial dilutions.

1. The coefficient of variation (CV)—also called the relative standard deviation (RSD)—is the ratio of the standard deviation to the mean.
2. There are also some disadvantages worth understanding for the coefficient of variation to be interpreted the way it’s supposed to be.
3. When we are presented with estimated values, the CV relates the standard deviation of the estimate to the value of this estimate.
4. The pulse rate and sodium are measured in completely different units, so comparing their standard deviation would be nonsense.
5. From here, you just need to divide the standard deviation by the mean to determine the coefficient of variation.
6. Other than helping when using the risk/reward ratio to select investments, it is used by economists to measure economic inequality.

(iii) Since the CV is estimated and has a distribution of its own, it may be prudent in some applications to employ not the point estimate but rather a more conservative estimate such as an upper percentile of the observed distribution of the CV. The CV expresses variation of an entity on a proportional scale that is easily interpretable when comparing variation among entities. If this remains the only goal for computing CVs, the only restriction for this computation concerns the scale on which entities are measured (Table 1, Box 1).

Coefficient of deviation in statistics is explained as the ratio of the standard deviation to the arithmetic mean, for instance, the expression standard deviation is 15 % of the arithmetic mean is the coefficient variation. Now that you know what the coefficient of variation and standard deviation are, let’s work through two examples of calculating the CV. If you find a coefficient of variation of 0.10 or 10%, the standard deviation is one-tenth or 10% of the mean. Included are explanations of the standard deviation and the mean as well as examples and common applications. Based on the calculations above, Fred wants to invest in the ETF because it offers the lowest coefficient (of variation) with the most optimal risk-to-reward ratio.