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Coefficient of Variation Formula

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Mastering the Coefficient of Variation: Meaning, Interpretation, and Practical Examples

Comprehensive Definition, Description, Examples & Rules 

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Introduction

The coefficient of variance is the ratio of the standard deviation to its mean. The higher the coefficient of variation, the greater the level of dispersion around the mean, and the coefficient of variation is expressed in terms of percentage. The coefficient of variance analysis is effective in human life and helps in the calculation, especially in the investment industry. 

Significance in Statistics

The major significance of the coefficient of variation in statistics includes:

  • It shows you the extent of variability with the mean of the population. 
  • It measures the data scales and ratio scale, which helps in the relative comparison of two measurements of statistics. 
  • It can also be used in comparison for data sets with different units or different means.

Understanding the Coefficient of Variation

The fundamental concept of the coefficient of variation is that it is a statistical measure of the relative dispersion of the data points in a data series around a mean. To simplify, it is the ratio of the standard deviation of the expression to its mean. 

The coefficient of variation meaning is the percentage between the standard deviation and the mean, while the higher the coefficient of variation, the greater the level of dispersion around the mean. 

Importance in Statistics

The coefficient of variation has a primary significance in Statistics:

  • It helps to measure the data scales and ratio scales that provide a relative comparison between the measurements in statistics. 
  • It also improves the statistical expression of the extent of variability to the population’s mean. 
  • You can also compare data sets with various units and means. 

You will use a coefficient of variation in data analysis when you want to compare two or more data sets with each other. The variation coefficient will help you find the ratio of the standard deviation to its mean. As this is an independent unit, the measurement will be compared among different units. 

Coefficient of Variation Formula

There are two formulas that you can use for calculating the coefficient of variation and these two formulas are:

  • Population Formula
  • Sample Formula

Population Formula

The population formula is:

Population Formula

The Population in statistics is the whole group which is under consideration and it is used to denote the completed data set. The formula is the standard deviation of the population mean. 

Sample Formula

The sample formula is:

Sample Formula

The sample formula represents the entire population of the study, and the sample mean is the coefficient of variation with its standard deviation on top. 

The standard deviation is in the numerator for both the population and sample formulas.

The step-by-step guide to follow is:

  • Check the sample set first.
  • Then, calculate the mean and standard deviation. 
  • Then, use any of the formulas of population or sample.

Example 

Two machines A and B of a factory show the following results about the number of workers and the wages paid to them.

No. of workers

5000

6000

Average monthly wages

$2500

$2500

Standard deviation

9

10

Using coefficient of variation formulas, find in which machine, A or B is there greater variability in individual wages.

Solution:

For this, we need to find the coefficient of variation. 

Coefficient of variation for A.

Using the coefficient of variation formula in statistics,

CV = (σ/μ) × 100, μ≠0

CV = (9/2500) × 100

CV = 0.36%

Now, the CV for B

CV = (σ/μ) × 100

CV = (10/2500) × 100

CV = 0.4%

A has CV = 0.36 and plant B has CV = 0.4

So, B has greater variability in individual wages.

Interpreting Coefficient of Variation

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 coefficient of variation values directly relates to data variability and relative risk as a high value will indicate that the data is highly variable and risk is low. A lower coefficient of variation will increase that the group is less variable, which means the risk is high.

A coefficient of variation of 0.5 will mean that the standard deviation is half as large as the mean, while one will mean that it is equal to the mean, and 1.5 will mean that the standard deviation is high.

Real-World Scenario:

The real-world scenario to justify the interpretation of the coefficient of variation is:

  • Investors effectively use it for calculation as the expected return on the investment is the word for the degree of variability and helps determine the risk, which will help you invest.

Coefficient of Variation Examples

The coefficient of variation example is:

Example 1: 

Find the Population of the coefficient of variation for the data set: 10, 12, 16, 18, 20

Solution:

The mean of the expression is: (10 + 12 + 16 + 18 + 20)/5 = 15.2

Standard Deviation is: √{(10 – 15.2)² + (12 – 15.2)² + (16 – 15.2)² + (18 – 15.2)² + (20 – 15.2)²}

= √(27.04 + 10.24 + 0.64 + 7.84 + 23.04)

= √(68.80

= 8.29

So, the Coefficient of Variation is: (Standard Deviation/ Mean) × 100

= 8.29/15.2 × 100

= 54.53 %

Example 2:

If the coefficient of variation is given as 20.75 and the mean is 22.6 then find the standard deviation.

Solution:

Coefficient of Variation = (Standard Deviation / mean) * 100

20.75 = (SD / 22.6) * 100

SD = 4.69

Answer: Standard deviation = 4.69

Practical Applications

The practical application areas where the coefficient of variation is useful include:

  • Finance: The finance and investment sector uses the coefficient of variation in Calculation and its most helpful area. Finance Calculation and determining the stock’s future is essential, which happens through the coefficient of variation.
  • Biology: Biology also involves an essential use of the coefficient of variation. Though it is unrelated to mathematical terms, particular biological calculations happen through the coefficient of variation.
  • Engineering: Civil engineers use the most mathematical calculations, and the primary use is the coefficient of variation in their mathematical calculations. 

The coefficient of variation plays a role in risk assessment and decision-making as it determines the variability of the particular data set and identifies the relative risk of using the data set.

The real-world case studies on Coefficient variation are:

  • CE Brown (Applied Multivariate of Statistics)
  • AG Bedeian (Organizational Research)
  • H Abdi (Encyclopedia of Research and Design)

Tips and Best Practices

You can effectively use a coefficient of variation in situations when you want to compare two or more different data sets. There are certain common mistakes which you can avoid while using the coefficient of variations, and these are:

  • It should not be employed with the variables measured through an interval scale as an interval scale cannot be computed in ratio.
  • It is also impossible to calculate when a variable’s mean is zero because the answer will be undefined, and the calculation will go wrong.

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. 

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Key Takeaways

  1. The coefficient of variation is essential to calculate when comparing two data sets. 

  2. It is impossible to calculate the coefficient of variation for non-numeric terms.

  3. You can face specific problems while calculating the coefficient of variation, especially when there is a zero in the mean.

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Frequently Asked Questions

You should effectively use the coefficient of variation when comparing two or more data sets and determining the variability and relative risk of using these data sets. 

No, using the coefficient of variation to determine the non-numeric data is impossible, as the standard deviation is only possible for numerical data. The non-numerical data cannot form a standard deviation, and the coefficient of variation cannot be formed without the standard deviation.

The primary difference between the coefficient of variation and the standard deviation is the coefficient of variation will measure the ratio of the standard deviation of the mean. While on the other hand, the standard deviation is used when calculating the difference spread values in a single data set. 

To interpret the result of the coefficient, you have to determine its mean in the standard deviation. A coefficient of variation of 0.5 will mean that the standard deviation is half at last as the mean, while a coefficient of variation of 1 will mean that the standard deviation is equal to the mean. A coefficient of variation of 1.5 will mean that the standard deviation is 1.5 larger than the mean.

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2D Shapes2cosacosb Formula30-60-90 Formulas3D ShapesAbsolute Value FormulaAcute AngleAcute Angle triangleAdditionAlgebra FormulasAlgebra of MatricesAlgebraic EquationsAlgebraic ExpressionsAngle FormulaAnnulusAnova FormulaAnti-derivative FormulaAntiderivative FormulaApplication of DerivativesApplications of IntegrationArc Length FormulaArccot FormulaArctan FormulaArea Formula for QuadrilateralsArea FormulasArea Of A Sector Of A Circle FormulaArea Of An Octagon FormulaArea Of Isosceles TriangleArea Of ShapesArea Under the Curve FormulaArea of RectangleArea of Regular Polygon FormulaArea of TriangleArea of a Circle FormulaArea of a Pentagon FormulaArea of a Square FormulaArea of a Trapezoid FormulaArithmetic Mean FormulaArithmetic ProgressionsArithmetic Sequence Recursive FormulaArithmetic and Geometric ProgressionAscending OrderAssociative Property FormulaAsymptote FormulaAverage Deviation FormulaAverage Rate of Change FormulaAveragesAxioms Of ProbabilityAxis of Symmetry FormulaBasic Math FormulasBasics Of AlgebraBinary FormulaBinomial Probability FormulaBinomial Theorem FormulaBinomial distributionBodmas RuleBoolean AlgebraBusiness MathematicsCalculusCelsius FormulaCentral Angle of a Circle FormulaCentral Limit Theorem FormulaCentroid of a Trapezoid FormulaChain RuleChain Rule FormulaChange of Base FormulaChi Square FormulaCirclesCircumference FormulaCoefficient of Determination FormulaCoefficient of Variation FormulaCofactor FormulaComplete the square formulaComplex numbersCompound Interest FormulaConditional Probability FormulaConeConfidence Interval FormulaCongruence of TrianglesCorrelation Coefficient FormulaCos Double Angle FormulaCos Square theta FormulaCos Theta FormulaCosec Cot FormulaCosecant FormulaCosine FormulaCovariance FormulaCubeCurated Maths Resources for Teachers – EdulyteCylinderDecimalsDifferential calculusDiscover the world of MathsEllipseEquilateral triangleEuler’s formulaEven numbersExponentsFractionFraction to decimalGeometric sequenceHeptagonHyperbolaIntegersIntegrationIntegration by partsLinesLocusMatricesNatural numbersNumber lineOdd numbersParallelogramPercentage formulaPerimeterPolygonPolynomialsPrismProbabilityPyramidPythagoras theoremRoman NumeralsScalene triangleSetsShapes NamesSimple interest formulaSlope formulaSolid shapesSphereSquareStandard deviation formulaSubtractionSymmetryTimeTrianglesTrigonometry formulaTypes of anglesValue of PiVariance formulaVectorVolume formulasVolume of a coneVolume of sphere formulaWhole numbers
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