Coefficient of variation is an important concept that allows you to predict variables within and outside data sets. While it has its roots in mathematics and statistics, coefficient of variation can be applied in different contexts including population studies and investments in the stock market.
So how does the coefficient of variation work as a statistical measure? To answer that question, let’s look at its different parts including its definition, calculation examples, and other related concepts.
What Is the Coefficient of Variation?
Also known as relative standard deviation, coefficient of variation is a statistical concept that accounts for relative variability in data sets. Specifically, it indicates the size of a standard deviation to its mean.
In survey research, coefficient of variation allows you to compare variability within significantly different groups; that is, the results from two systematic investigations that do not have similar grading parameters or measures of value.
For example, if the coefficient of variation of research A is 14% and that of research B is 20%, you can say that research B has a higher degree of variation to its mean.
How to Calculate the Coefficient of Variation in a Survey
The standard formula for calculating the coefficient of variation is as follows:
Coefficient of Variation (CV) = (Standard Deviation/Mean) × 100.
Depending on the context of the application, you can make slight changes to this formula. For example, if you want to calculate CV in financial research, you can rewrite the formula as:
Coefficient of Variation = (Volatility ÷ Expected Returns) × 100%
Let’s look at how to apply this formula in survey research.
An organization conducts market research on different groups and presents the following results:
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Target Audience A
Mean: 60
Standard Deviation: 10
Target Audience B
Mean: 50
Standard Deviation: 7.5
To select the more suitable market for investments, they can compare the coefficient of variation of both options.
Coefficient of Variation (A) = (60÷10) × 100% = 600%
Coefficient of Variation (B) = (50÷7.5) × 100% = 667%
Based on this result, the organization decides to invest in target audience A because it offers a lower coefficient of variation.
Use Cases/Industrial Applications of Coefficient of Variation
Application 1
Financial analysts use coefficients of variation to evaluate investment risks for better decision-making. When presented with multiple investment options, coefficient of variation helps you compare both options in terms of risks and returns and choose the option with the highest ROI.
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Suppose investment A has a standard deviation of 5% and a 10% ROI, while investment B has an estimated ROI of 15% and a standard deviation of 10%. By applying the COV formula, you discover that investment A has lower investment risks.
Application 2
Coefficient of variation can also be used to measure the viability of new markets before an organization launches a new product, service, or outlet. You can compare the projected market penetration costs for two territories and choose the option that has lesser variations.
Application 3
Researchers use coefficients of variation to compare outcomes of systematic investigations across different populations. For example, you can use COV to measure the variability of spending among high-income earners and low-income households.
Solved Examples Involving the COV Formula
Example 1
A middle-income earner is presented with the following investment options:
Option A: Cryptocurrency
Return on Investment: 25%
Volatility: 15%
Option B: Treasury Bills
Return on Investment: 5%
Volatility: 0.75%
COV = (Volatility ÷ ROI) × 100
COV (Option A) = (15% ÷ 25%) × 100 = 60%
COV (Option B) = (0.75% ÷ 5%) × 100 = 15%
Based on this, option B presents lower volatility for investors.
Example 2
After conducting a systematic investigation on high-income earners and low-income earners in a community, a researcher has the following results:
High-Income Earners
Standard Deviation: $100,000
Mean: $600,000
Low-income Earners
Mean: $35,000
Standard Deviation: $5,000
Coefficient of Variation (for High Income Earners) = ($100,000 ÷ $600,000) × 100 = 16.6%
Coefficient of Variation (for Low Income Earners) = ($5,000 ÷ $35,000) × 100 = 14.3%
The Practical Limitation of the Coefficient of Variation Formula
Coefficient of variation measures variability using ratio scales. This means it cannot be used for constructing confidence intervals for the mean, unlike standard deviation.
Understanding Coefficient of Variation Formula and Related Concepts
As you dive deeper into the coefficient of variation, you’d come across several related concepts, including mean, standard deviation, and dispersion. Understanding these related concepts would help you apply coefficients of variation to your data sets accurately. Let’s discuss some of them in this section.
Dispersion
Dispersion or variability accounts for the distribution of numerical values within a statistical function. Researchers depend on variability to know how far apart data points lie from each other and the center of a distribution.
Dispersion allows the research to know how homogeneous or heterogeneous the data sets are while interpreting the variability of the distinct values. You can measure distribution in research data using range, variance, and standard deviation.
Types of Dispersion
Statisticians split dispersion into two, which are:
- Absolute Measure of Dispersion
- Relative Measure of Dispersion
1. Absolute Measure of Dispersion
Absolute measures of dispersion are used to determine the amount of distribution within a single set of observations. By design, the results from absolute measures of dispersion are always in the same measuring units as the original data sets. For example, if the data points are in meters, the absolute measures would also be meters.
Depending on the purpose of your research and numerical data sets, you can use one or more of these types of absolute measures of dispersion:
- Range
- Variance and Standard Deviation
- Quartiles and Quartile Deviation
- Mean and Mean Deviation
Pros of Using Absolute Measures of Dispersion
- They are relatively simple to understand and calculate.
- Absolute measures of dispersion limit any distortions caused by extreme scores in data sets, especially when you depend on mean deviation.
Cons of Using Absolute Measures of Dispersion
- They can yield inappropriate or impractical results.
- The computation processes for absolute measures of dispersions can be complicated, especially if you’re dealing with a large data set.
2. Relative Measure of Dispersion
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.
Common relative dispersion methods include:
- Coefficient of Range
- Coefficient of Variation
- Coefficient of Standard Deviation
- Coefficient of Quartile Deviation
- Coefficient of Mean Deviation
Pros of Using Relative Dispersion Methods
- Relative dispersion methods allow you to compare two or more statistical series.
- They help researchers to control the variability of a phenomenon.
Cons of Using Relative Dispersion Methods
- They can result in misinterpretations and generalizations in data sets.
- They are liable to yield inappropriate results as there are different methods of calculating the dispersions.
Mean
Mean refers to the average value of a data set. You can also think of it as the most common variable in a collection of observations for research. It can be used for linear and straightforward data sets, as well as more complex observations.
Statisticians refer to mean as a measure of central tendency because it accounts for all the values in a data set, especially extreme variables. This makes it easy for you to identify the ideal midpoint of your research data.
While the arithmetic mean is the most common type of this measure of central tendency, there’s also weighted mean, geometric mean (GM), and harmonic mean (HM).
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How to Calculate Mean
Mean = Total of all variables ÷ number of variables in the sample size
Let’s put this formula to work.
Suppose an organization has 1,500 as the total of 15 variables in its research sample size. In this case, the mean of the data set is 100.
Pros of Using Mean in Statistics
- It provides an objective presentation of the different variables in a data set.
- It limits the influence of extreme values in large research samples.
Cons of Using Mean in Statistics
- It is sensitive to extreme values in a small data set.
- Mean is not the most appropriate measure of central tendency for skewed distribution.
Standard Deviation
Standard deviation is somewhat similar to dispersion and variability. However, in this case, standard deviation measures the distribution of values in a data set related to its mean. Once you know the variance or dispersion for your data, you can take the square root of this value to determine the standard deviation.
A high standard deviation shows you that individual variables are generally far from the mean in typical data distributions. In contrast, a low standard deviation indicates that data values are closely clustered around the mean.
How to Calculate Standard Deviation in Research
Step 1: Calculate the arithmetic mean of your data set.
Step 2: Subtract the mean from each score to get the deviations from the mean.
Step 3: Square each deviation from the mean. This will result in positive numbers.
Step 4: Find the sum of the squares deviations.
Step 5: Find the variance of the data sets.
Step 6: Take the square root of the variance to get the standard deviation.
The basic standard deviation formula is as follows:
Where;
s = sample standard deviation
∑ = sum of…
X = each value
x̅ = sample mean
n = number of values in the sample
Pros of Using Standard Deviation in Survey Research
- Standard deviation gives you a better idea of your data’s variability than more straightforward measures of variation.
- By squaring the differences from the mean, standard deviation reflects uneven dispersion more accurately.
Cons of Standard Deviation
- It is susceptible to extreme values in data sets.
- Standard deviation doesn’t give a full range of the data.
Coefficient of Variation vs. Standard Deviation
- Definition
Standard deviation is a statistical value that accounts for the dispersion of a data set regarding its mean. At the same time, the coefficient of variation is the ratio of standard deviation to its mean value.
- Purpose
Both standard deviation and coefficient of variation calculate the variations in an original data set. However, the coefficient of variation goes further to determine the ratio of the variability of the data set’s mean.
- When to Use
If you want to compare the variability of measurements made in different units, then the coefficient of variability is a valuable metric in this case. However, calculating standard deviation can be helpful when you want to determine the margin of error or volatility in your data sets.
- Advantages of Coefficient of Variation
One of the significant advantages of the coefficient of variation is that it is unitless, and you can apply it to any given quantifiable observation. This allows you to compare the degree of variation between two different data sets.
- Advantages of Standard Deviation
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.
Coefficient of Variation vs. Variance
- Definition
Variance is a measure of variability that shows you the degree of spread in your data set using larger units like meters squared. On the other hand, coefficient of variation measures the relative distribution of data points around the mean.
- When to Use
Use variance or variance tests to assess the differences between populations or groups in your research. Meanwhile, coefficient of variation allows you to compare the degree of variability between different data sets.
- Advantages of Variance
Variance helps you to gain helpful information about a data set for better decision-making. 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.
- Advantages of Coefficient of Variation Over Variance
Coefficient of variation helps to measure the degree of consistency and uniformity in the distribution of your data sets. Unlike variance, it doesn’t depend on the measurement unit of the original data, which allows you to compare two different distributions.
Other FAQs on Coefficient of Variation
1. Does COV Have Units?
No. Coefficient of variation is a unitless measure of relative dispersion. The absence of units allows COV to be used to compare variability across mutually exclusive data sets.
2. What Is a Bad Coefficient of Variation?
If the coefficient of variation is greater than 1, it shows relatively high variability in the data sets. On the flip side, a CV lower than 1 is considered to be low-variance.
3. What Is an Acceptable Coefficient of Variation?
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.
4. Can the Coefficient of Variation be Negative?
Yes. If the mean of your data is negative, then the coefficient of variation will be negative. However, this typically means that the coefficient of variation is misleading.
5. What Is the Formula for Deriving the Coefficient of Variation?
Coefficient of Variation = (Standard Deviation ÷ Mean) × 100%
Conclusion
In this article, we’ve discussed the co-efficient of variation and showed you how it differs from concepts like mean deviation, variance and standard deviation. While you wouldn’t always have to apply a coefficient of variation to your data sets, it pays to know how it works and the difference it makes in research.