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    • Coefficient of Variation: The Coefficient of Variation is a measure of Relative variability. It is the Ratio of the Standard Deviation to the Mean. It is a useful method for comparing the Degree of Variation from One Data Series to another, even if the means are drastically different from one another. It has the following characteristics: -Measure of relative variation - Shows Variation relative to mean - Used to compare 2 or more groups   How to calculate Coefficient of Variation: The main purpose of finding the Coefficient is used to study of Quality assurance by measuring the spread of the Population data of a Probability or frequency distribution or by determining the content or Quality of the sample data of substances   Calculation of Coefficient of variation: - Calulate the Mean of the Data Set - Calculate the Sample SD of the Data Set - Finding the Ratio of the Sample SD to mean brings the Coefficient of Variation [CV] of the Data set   Formulas to calculate coefficient of variation:
       
      Examples for Coefficient of Variation: Calculate the relative variability (coefficient of variance) for the samples 60.25, 62.38, 65.32, 61.41, and 63.23 of a population

      Solution:
      Step by step calculation:
      Step 1: calculate mean
      Mean = (60.25 + 62.38 + 65.32 + 61.41 + 63.23)/5
      = 312.59/5
      = 62.51

      Step 2: calculate standard deviation
      = √( (1/(5 - 1)) * (60.25 - 62.51799)2 + (62.38 - 62.51799)2 + (65.32 - 62.51799)2 + (61.41 - 62.51799)2 + (63.23 - 62.51799)2)
      = √( (1/4) * (-2.267992 + -0.137989992 + 2.802012 + -1.107992 + 0.712012))
      = √( (1/4) * (5.14377 + 0.01904 + 7.85126 + 1.22764 + 0.50695))
      = √ 3.68716
      σ = 1.92

      Step 3: calculate coefficient of variance
      CV = (Standard Deviation (σ) / Mean (μ))
      = 1.92 / 62.51
      = 0.03071     2. A company has two sections with 40 and 65 employees respectively. Their average weekly wages are $450 and $350. The standard deviation are 7 and 9. (i) Which section has a larger wage bill?. (ii) Which section has larger variability in wages? 
      Solution: 
      (i) Wage bill for section A = 40 x 450 = 18000 
      Wage bill for section B = 65 x 350 = 22750 
      Section B is larger in wage bill. 
      (ii) Coefficient of variance for Section A = 7/450 x 100 =1.56 % 
      Coefficient of variance for Section B = 9/350 x 100 = 2.57% 
      Section B is more consistent so there is greater variability in the wages of section A. 
         
    • The Coefficient of Variation (CV) that is also known as the Relative Standard Deviation (RSD) is the ratio of the Standard Deviation of a Dataset to its Mean, popularly expressed as a percentage.   The CV is a useful metric to compare variations of two datasets with different means. This metric has the advantage of all ratio coefficients in that it acts as a “common denominator” when comparing diverse data sets.   Some of the relevant features of the CV are that it is independent of the order of values in the dataset and that it is relevant with only positive values of the dataset.   The applications of the CV are many and include:   1.    Evaluation of risk of investments vis-à-vis the return – Lower the CV, better the risk – return match 2.    Assess the homogeneity of solid powder mixtures – Closer the CV to the defined norm, more homogeneous is the mixture 3.    Measuring specific properties of chemicals or proportions of specific materials in mixtures 4.    Calculation of economic disparity of a community or a group 5.    Comparison of performance of two batches in a batch processing industry   The CV can used to test hypotheses through Levene’s test.   The general interpretation of the CV is that lower the CV lesser the variation relative to the mean and therefore a lower value of CV is preferable.   While the advantages of CV are many, one of its disadvantages is that it is usable with only parameters on a ratio scale but not on an ordinal, value or categorical scales. Further if the dataset consists of both positive and negative values, the mean tends to zero and CV tends to infinity. If the two datasets being compared, contain values or on a scale related to one another, then the CV would be different for both the datasets in spite of the data sets being related. (E.g. The CVs of two data sets measuring the temperature of the same substances but expressed as Celsius in one data set and as Fahrenheit in another).
    • Coefficient of Variation (CoV) is the ratio of Standard Deviation and the Mean. It is a unitless ratio. CoV is an overall indicator of relative risk. For example, there are two different investment options. Stock A has an expected return of 15% and Stock B has an expected return of 10%. Stock A has a standard deviation of 10% whereas Stock B has a standard deviation of 5%. Which one is a better investment? If we compare the CoV of both the options, it shows that Stock B is a better option, since CoV of Stock B is 5/10 i.e. 0.5 whereas CoV for Stock A is 10/15 i.e. 0.67. Lesser the CoV more consistent are the returns.
    • Dear all, this is classic example of good learning initiative for all of us. We all know Ishikawa diagram is one of the easiest tool to use for RCA.   However alone we may not think through in this detail to understand pitfalls and misuse of such a simple but effective tool.   Most of the answers addressed what and how of Fishbone diagram and also addressed the pitfalls that might render the use of this tool ineffective.   The best three answers were from Mr. Venugopal R., Mr. Mohan P.B. and Mr. Ronak.  The most suitable answer addressing the misuse of the tool was from Mr. Mohan P.B..     Congratulations to you Mr. Mohan.
    • The Coefficient of variation (CV) is basically the ratio of the standard deviation to the mean in a given data set. It is used as a measure of relative variability and allows to compare the range or spread of many data sets. Just to understand it very easily let us take the examples of a QSR which is trying to find the best bet to open outlet  , between 2 territories  with favourable traits, proport- Traits like population, SocioEconomic level of population, Competition, Prospect growth in the territory etc. The Real Estate team has cited 20  locations and their rentals in both territories. NOW, the decision is narrowed down on the rentals of the sites as the sales projected in both the territories is more or less proportionate to the respective rentals. It would now be prudent to open the outlets in the territory where the difference in rentals are not very high amongst the outlets. This helps to budget the costs and the disparity of rentals is not much and hence the allocations of budgets for project work become almost even for all outlets.  The management wants to understand in which territory the variation in rentals is higher. Then the territory with lesser variation in rentals will be the choice to open outlets.   Territory 1 Territory 2 Average Rentals (Mean)- Average Rentals (Mean)- 120000 200000 Standard Deviation in Rentals Standard Deviation in Rentals 2000 3000 Coefficient of Variation Coefficient of Variation =2000/120000= 0.016 =3000/200000 = 0.015   In territory 1, The Average or mean of the rentals is Rs. 1.20 Lacs and the standard deviation is 2000/- . Ie. Rentals of most of the outlets are in the range from 1.22 Lacs to 1.18 Lacs In Territory 2 , The Average or Mean of the rentals is 2 Lacs and the standard deviation is 3000/-ie. Rentals of most of the outlets are in the range from 2.03 lacs to 1.97 Lacs. It is obvious from the coefficient of variation that the range of rentals are higher in Territory 1. The management will hence try to work on the Territory #2   Likewise, CV is used in many other situations like: -          To compare relative risks in process during the Design stage as it be applied to any kind of probability distribution. -          Since it is a statistical measure that is normalized and hence has no dimension, It is used as a measure of dispersion and used instead of standard deviation to compare data sets with different measures and significantly different means. -          Most commonly CV is used to measure the volatility in the prices of stocks and securities   In conclusion , is useful in any study that demonstrates exponential distribution i.e. It helps to show when distributions are considered low – variance and when they are said to be high – variance.
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