Two of the relative measures of Standard Deviation are Coefficient of Standard Deviation and Coefficient of Variation. When we want to compare two or more data sets, the coefficient of variation is used. And because it’s independent of the unit in which the measurement was taken, it can be used to compare data sets with different units or widely different means. 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. Standard deviation is somewhat similar to dispersion and variability.
Standard Deviation
On the other hand, coefficient of variation measures the relative distribution of data points around the mean. The coefficient of variation (relative standard deviation) is a statistical measure of the dispersion of data points around the mean. The coefficient of variation meaning metric is commonly used to compare the data dispersion between distinct series of data. Unlike the standard deviation that must always be considered in the context of the mean of the data, the coefficient of variation provides a relatively simple and quick tool to compare different data series.
Sample or Population Data
Temperature measurements in Celsius or Fahrenheit, for instance, are interval scales, as a temperature of 0°C or 32°F does not signify the complete lack of thermal energy. One significant limitation of the coefficient of variation arises when dealing with data sets where the mean value approaches zero. In such cases, the CV can become extremely sensitive to even minor fluctuations in the mean, potentially leading to misleading or unreliable interpretations. The CV, also called relative standard deviation, is a scale-free stats metric that quantifies how data scatters around the average.
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. For example, consider a risk-averse investor who wishes to invest in an exchange-traded fund (ETF), which is a basket of securities that tracks a broad market index. The investor selects the SPDR S&P 500 ETF (SPY), the Invesco QQQ ETF (QQQ), and the iShares Russell 2000 ETF (IWM). Then, the investor analyzes the ETFs’ returns and volatility over the past 15 years and assumes that the ETFs could have similar returns to their long-term averages.
Coefficient of Variation (CV) Formula
- Adam Hayes, Ph.D., CFA, is a financial writer with 15+ years Wall Street experience as a derivatives trader.
- The coefficient of variation (Cᵥ) is the ratio of the standard deviation to the mean, sometimes expressed as a percentage.
- The result of your coefficient of variation will be in percentage, and if your answer is in decimal form, then you will use the two digits after your decimal and the follow-up rule to write your answer.
- Variance treats all numbers in a set the same, regardless of whether they are positive or negative, which allows you to account for the most minute variability in data sets.
A high Coefficient of variation interpretation will indicate that the group is more variable, while a low value of the coefficient of variation will suggest that the group is less variable. It is how you can calculate and interpret the coefficient of variation as the standard deviation is a Statistics measuring, so it is estimated in terms of variance. You can also interpret it as the higher the coefficient of variation, the greater the level of dispersion around its mean. The Population in statistics is the whole group which is under consideration and it is used to denote the completed data set.
When asked to calculate the variance or standard deviation of a set of data, assume – unless otherwise instructed – this is sample data and therefore calculating the sample variance and sample standard deviation. One way to describe spread or variability is to compute the standard deviation. In the following section, we are going to talk about how to compute the sample variance and the sample standard deviation for a data set. Coefficient of variation is a dimensionless measure of dispersion that gives the extent of variability in data.
Well, actually, the sample mean is the average of the sample data points, while the population mean is the average of the population data points. As you can see in the picture below, there are two different formulas, but technically, they are computed in the same way. In the field of statistics, we typically use different formulas when working with population data and sample data. This is particularly useful when evaluating investments with vastly different expected returns, as the CV accounts for the disparities in means, enabling a more equitable comparison of risk-to-reward ratios. By comparing the relative volatility of different assets or investment vehicles, investors can make informed decisions that align with their risk tolerance and desired returns. Attempting to calculate and interpret the CV for interval scale data can lead to erroneous conclusions, as the underlying assumptions of the ratio calculations are violated.
It is expressed as the ratio of the standard deviation to the mean. The coefficient of variation is a dimensionless quantity and is usually given as a percentage. It helps to compare two data sets on the basis of the degree of variation. On the other hand, researchers use relative measures of dispersion to compare the distribution of two or more data sets. Unlike absolute measures of dispersion, relative measures do not consider the unit of the original observation. When applying relative measures to data sets, you’d get a ratio-like result that also passes as a coefficient.
As you compare prices of various brands, some offer price per roll while others offer price per sheet. What happens to measures of variability if we add or multiply each observation in a data set by a constant? We learned previously about the effect such actions have on the mean and the median, but do variation measures behave similarly? The article explains what variance means, how to calculate it, how to use the formula and the main differences between variance and standard deviation.
Guide on the differences in numerical and categorical data as it relates with definitions, examples, types, data collection, advantage,… The coefficient of variation differs based on the composition of data points in your observation. In general, a coefficient of variation between 20–30 is acceptable, while a COV greater than 30 is unacceptable. Standard deviation gives you a clear idea of the distribution of data in an observation. It also serves as a shield against the effects of extreme values or outliers in quantifiable observation.