Coefficient of Variation Definition, Formula, and Example

The intent of this article is to introduce the mathematical relationship between the CV and the frequency of k-fold or more-disparate assay values when the same sample is subjected to repeated measurements. We also demonstrate how this relationship can be used to address practical problems in a clinical laboratory. In serological assays a twofold difference in measurements of the same sample has been widely regarded as the upper limit on acceptable variability, and the frequency of such differences among pairs of repeated measurements has been proposed as an apt index for assay variability (5). Wood (4) showed the mathematical relationship between that frequency and the size of the SD of repeated assay measurements, under the assumption that the logarithm of measurements is normally distributed. The tables he provided indicate how small an SD of the log measurements must be in order to ensure that only some predetermined fraction of pairs of measurements differ by a factor of two or more.

Example of Coefficient of Variation (CV) for Selecting Investments

1. Statistical analyses in ecology and evolution often involve the calculation of summary statistics to facilitate interpretation.
2. For example, if you have a CV of 10%, it means that the standard deviation is 10% of the mean.
3. 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.
4. The tables he provided indicate how small an SD of the log measurements must be in order to ensure that only some predetermined fraction of pairs of measurements differ by a factor of two or more.
5. One limitation is that the CV is only meaningful for data that are positive and have a meaningful zero point.
6. For example, an investor who is risk-averse may want to consider assets with a historically low degree of volatility relative to the return, in relation to the overall market or its industry.

It’s used with both inside and outside data sets and it can be used in several different contexts. A few of the most common include various types of population studies as well as investments made in the stock market. The coefficient of variation (relative standard deviation) is a statistical measure of the dispersion of data points around the mean. The metric is commonly used to compare the data dispersion between distinct series of data.

Associated Data

Thus the interpretation of variability is always in terms of original values. On the other hand, Wood’s system, founded on the SD, requires the SD to be calculated from the transformed assay values and is dependent on which logarithm base is used. For any scales where the zero point is not defined (nominal scale and ordinal scale) or arbitrarily chosen (interval scale), it is not meaningful to calculate a CV and talk about proportional changes. Similarly, the calculation of the CV may be compromised for any scale where the mean can be equal to 0 (signed‐ratio scale or difference scale; in the difference scale, the zero point corresponds to ln(1)).

Notice that a clearly defined zero point does not necessarily mean that 0 has a clear biological meaning. For example, if we use gram or centimeter to measure the size of some individual organisms, these two measurements have a clearly defined 0, but we do not expect to observe individuals of 0 g or 0 cm. Finally, for absolute scales such as probability, the calculation and the interpretation of the CV may be strongly affected by the distribution of the data and the mean‐standard deviation relationship (see main text). Table 1 summarizes the different scales, their permissible transformation, and whether the calculation of CVs is meaningful.

As Standard Deviation is an absolute measure of dispersion, one cannot use it for comparing the variability of two or more series when they are expressed in different units. Therefore, in order to compare the variability of two or more series with different units it is essential to determine the relative measure of Standard Deviation. Two of the relative measures of Standard Deviation are Coefficient of Standard Deviation and Coefficient of Variation. Using the coefficient of variation will be extremely helpful for investors when analyzing the risk and reward ratio for certain investments.

Rate this article

For example, if your data have a few very large values that increase the mean and the standard deviation, the CV may not reflect the true variability of most of the data. Analysis would be undertaken based on the 15-year historical information that the investor used to initially make their decision. Using the coefficient of variation calculations, they can determine which ETFs have the best risk and reward ratios. As well, they would be able to see and compare the better trade-off for risk and return between each of the three ETFs being compared.

1. When we want to compare two or more data sets, the coefficient of variation is used.
2. 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.
3. Understanding the causes for such nonproportionality may become critical for interpreting differences in variation among quantitative traits.
4. 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.
5. 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.
6. However, it would be desirable for the sake of comparability among laboratories to have laboratories in specific research areas conform to some consensus, if possible, on the choice of k.

However, the low coefficient is not favorable when the average expected return is below zero. The standard deviation is a statistic that measures the dispersion of a data set relative to its mean. It is used to determine the spread of values in a single data set rather than to compare different units. The CV is useful for comparing scatter of variables measured in different units.

To calculate the coefficient of variation, first find the mean, then the sum of squares, and then work out the standard deviation. With that information at hand, it is possible to calculate the coefficient of variation by dividing the standard deviation by the mean. When the mean value is close to zero, the CV becomes very sensitive to small changes in the mean. Using the example above, a notable flaw would be if the expected return in the denominator is negative or zero.

In short, the standard deviation measures how far the average value lies from the mean, whereas the coefficient of variation measures the ratio of the standard deviation to the mean. It is defined as the standard deviation of a group of values divided by their mean. Often that ratio is multiplied by 100 to express the coefficient of variation as a percent (abbreviated %CV). Standard deviation formula helps us to find the values of a particular data that is dispersed. In this, higher values mean that the values are far from the average mean as well as the lower values mean that values are very close to their average mean. Calculating the CV is allowed if all the numbers in the distribution have the coefficient of variation meaning same sign (notice that this could generate negative CVs).

Similar ratios

In contrast, the actual value of the CV is independent of the unit in which the measurement has been taken, so it is a dimensionless number. For comparison between data sets with different units or widely different means, one should use the coefficient of variation instead of the standard deviation. The coefficient of variation (CV) is the ratio of the standard deviation to the mean.

Using Mean‐Standardization to Compare Evolvability or Phenotypic Plasticity

Nomogram for relating the CV to the probability that two assay measurements from the same analyte sample will differ by a factor k or more. Plus, even if there is a scenario where the mean of a variable isn’t zero and there are positive and negative values, the coefficient of variation could be misleading. When you’re working with a data set, mean simply refers to the average value. It’s important to evaluate the mean because it accounts for all of the different values included in a data set. Ultimately, this makes it easier to identify the midpoint of any research or data. To convert the coefficient into a percentage, just multiply the ratio of the standard deviation to the mean by 100.

Unlike absolute measures of dispersion—such as quartiles, mean absolute deviation, variance, and standard deviation—the coefficient of variation is a relative measure of dispersion. It compares how large the standard deviation is relative to the mean in proportional terms rather than absolute terms. By determining the coefficient of variation of different securities, an investor identifies the risk-to-reward ratio of each security and develops an investment decision. Generally, an investor seeks a security with a lower coefficient (of variation) because it provides the most optimal risk-to-reward ratio with low volatility but high returns.