coefficient of variance's significance












2














As far as I know, the coefficient of variance (CV) is used for measuring consistency of any variable. But should one always depend on CV for taking decisions, especially when means the are different?



For instance, there are 2 companies: A and B. Company A has a mean profit of $1000 and CV is 0.816%. Company B has a mean profit of $7666.67, but CV is 26.8%.



Which company should one invest in?










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    2














    As far as I know, the coefficient of variance (CV) is used for measuring consistency of any variable. But should one always depend on CV for taking decisions, especially when means the are different?



    For instance, there are 2 companies: A and B. Company A has a mean profit of $1000 and CV is 0.816%. Company B has a mean profit of $7666.67, but CV is 26.8%.



    Which company should one invest in?










    share|cite|improve this question



























      2












      2








      2







      As far as I know, the coefficient of variance (CV) is used for measuring consistency of any variable. But should one always depend on CV for taking decisions, especially when means the are different?



      For instance, there are 2 companies: A and B. Company A has a mean profit of $1000 and CV is 0.816%. Company B has a mean profit of $7666.67, but CV is 26.8%.



      Which company should one invest in?










      share|cite|improve this question















      As far as I know, the coefficient of variance (CV) is used for measuring consistency of any variable. But should one always depend on CV for taking decisions, especially when means the are different?



      For instance, there are 2 companies: A and B. Company A has a mean profit of $1000 and CV is 0.816%. Company B has a mean profit of $7666.67, but CV is 26.8%.



      Which company should one invest in?







      variance coefficient-of-variation






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      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Dec 15 '18 at 16:50









      Karolis Koncevičius

      1,65321425




      1,65321425










      asked Dec 15 '18 at 12:40









      nafisnafis

      111




      111






















          2 Answers
          2






          active

          oldest

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          4














          CV is a measure of the spread of a distribution, adjusted for the mean of the variable - it is defined as the standard deviation divided by the mean. So, it is only useful in situations where the means are different - if the means were the same, you could just use the standard deviation.



          However, CV becomes useless in some situations - e.g. when some of the values are negative.



          As to your specific question, this is far too little information to decide which company to invest in. And, since profit can be negative, the CV may be nonsensical. Suppose, for example, that company C has profit over the last three years of $1,000, $0 and -$1,000 (a loss of $1,000). Then the CV is undefined because the mean is 0. But change the first profit to $1,001 and the CV is now 3001.5 (or 300,150%). Or make the the loss in year 3 one dollar more and the CV is negative.






          share|cite|improve this answer





























            0














            In addition to the very informative answer that Peter provided above, you should also take into serious consideration all of the descriptive statistics derived from your sample. Especially when it comes to optimum investment option selecting, skewness of your data plays crucial role in deciding which one would be the most promising in terms of profitability.



            For instance, suppose that you have this sample: $1000,$1500,$1300,$1400,$1350,$1550,$1250,$1100,$10000,$1150,$1280. This sample implies CV=38,15% and mean profit=$2080



            Then we have another sample:
            $2000,$2160,$1960,$2200,-$4000,$8160,-$10000,$14160,-$15000,$19160,$2080 wich implies CV=141% and mean profit=2080



            At first glance,whereas both of the samples have the same mean, we would opt for the first option as the optimum investment since it implies the smallest CV, but if you examine more thoroughly both of the data, you will find out that in the first sample we have an extreme value ($10000) wich significantly affects the distribution of the data (positive skewness),fact that renders them unreliable.
            As far as the second sample is concerned, we can distinguish from the graph (and from the descriptive statistics of course) that the data is normally distributed around the mean, fact that makes them more consistent to rely on and take decissions based on them, even though it has larger volatility.



            Ιn conclusion, the real challenge of a researcher is whether he/she should exclude or not the extreme values of the sample and how he/she justify such action.






            share|cite|improve this answer





















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              2 Answers
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              2 Answers
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              4














              CV is a measure of the spread of a distribution, adjusted for the mean of the variable - it is defined as the standard deviation divided by the mean. So, it is only useful in situations where the means are different - if the means were the same, you could just use the standard deviation.



              However, CV becomes useless in some situations - e.g. when some of the values are negative.



              As to your specific question, this is far too little information to decide which company to invest in. And, since profit can be negative, the CV may be nonsensical. Suppose, for example, that company C has profit over the last three years of $1,000, $0 and -$1,000 (a loss of $1,000). Then the CV is undefined because the mean is 0. But change the first profit to $1,001 and the CV is now 3001.5 (or 300,150%). Or make the the loss in year 3 one dollar more and the CV is negative.






              share|cite|improve this answer


























                4














                CV is a measure of the spread of a distribution, adjusted for the mean of the variable - it is defined as the standard deviation divided by the mean. So, it is only useful in situations where the means are different - if the means were the same, you could just use the standard deviation.



                However, CV becomes useless in some situations - e.g. when some of the values are negative.



                As to your specific question, this is far too little information to decide which company to invest in. And, since profit can be negative, the CV may be nonsensical. Suppose, for example, that company C has profit over the last three years of $1,000, $0 and -$1,000 (a loss of $1,000). Then the CV is undefined because the mean is 0. But change the first profit to $1,001 and the CV is now 3001.5 (or 300,150%). Or make the the loss in year 3 one dollar more and the CV is negative.






                share|cite|improve this answer
























                  4












                  4








                  4






                  CV is a measure of the spread of a distribution, adjusted for the mean of the variable - it is defined as the standard deviation divided by the mean. So, it is only useful in situations where the means are different - if the means were the same, you could just use the standard deviation.



                  However, CV becomes useless in some situations - e.g. when some of the values are negative.



                  As to your specific question, this is far too little information to decide which company to invest in. And, since profit can be negative, the CV may be nonsensical. Suppose, for example, that company C has profit over the last three years of $1,000, $0 and -$1,000 (a loss of $1,000). Then the CV is undefined because the mean is 0. But change the first profit to $1,001 and the CV is now 3001.5 (or 300,150%). Or make the the loss in year 3 one dollar more and the CV is negative.






                  share|cite|improve this answer












                  CV is a measure of the spread of a distribution, adjusted for the mean of the variable - it is defined as the standard deviation divided by the mean. So, it is only useful in situations where the means are different - if the means were the same, you could just use the standard deviation.



                  However, CV becomes useless in some situations - e.g. when some of the values are negative.



                  As to your specific question, this is far too little information to decide which company to invest in. And, since profit can be negative, the CV may be nonsensical. Suppose, for example, that company C has profit over the last three years of $1,000, $0 and -$1,000 (a loss of $1,000). Then the CV is undefined because the mean is 0. But change the first profit to $1,001 and the CV is now 3001.5 (or 300,150%). Or make the the loss in year 3 one dollar more and the CV is negative.







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered Dec 15 '18 at 14:07









                  Peter FlomPeter Flom

                  74.6k11105202




                  74.6k11105202

























                      0














                      In addition to the very informative answer that Peter provided above, you should also take into serious consideration all of the descriptive statistics derived from your sample. Especially when it comes to optimum investment option selecting, skewness of your data plays crucial role in deciding which one would be the most promising in terms of profitability.



                      For instance, suppose that you have this sample: $1000,$1500,$1300,$1400,$1350,$1550,$1250,$1100,$10000,$1150,$1280. This sample implies CV=38,15% and mean profit=$2080



                      Then we have another sample:
                      $2000,$2160,$1960,$2200,-$4000,$8160,-$10000,$14160,-$15000,$19160,$2080 wich implies CV=141% and mean profit=2080



                      At first glance,whereas both of the samples have the same mean, we would opt for the first option as the optimum investment since it implies the smallest CV, but if you examine more thoroughly both of the data, you will find out that in the first sample we have an extreme value ($10000) wich significantly affects the distribution of the data (positive skewness),fact that renders them unreliable.
                      As far as the second sample is concerned, we can distinguish from the graph (and from the descriptive statistics of course) that the data is normally distributed around the mean, fact that makes them more consistent to rely on and take decissions based on them, even though it has larger volatility.



                      Ιn conclusion, the real challenge of a researcher is whether he/she should exclude or not the extreme values of the sample and how he/she justify such action.






                      share|cite|improve this answer


























                        0














                        In addition to the very informative answer that Peter provided above, you should also take into serious consideration all of the descriptive statistics derived from your sample. Especially when it comes to optimum investment option selecting, skewness of your data plays crucial role in deciding which one would be the most promising in terms of profitability.



                        For instance, suppose that you have this sample: $1000,$1500,$1300,$1400,$1350,$1550,$1250,$1100,$10000,$1150,$1280. This sample implies CV=38,15% and mean profit=$2080



                        Then we have another sample:
                        $2000,$2160,$1960,$2200,-$4000,$8160,-$10000,$14160,-$15000,$19160,$2080 wich implies CV=141% and mean profit=2080



                        At first glance,whereas both of the samples have the same mean, we would opt for the first option as the optimum investment since it implies the smallest CV, but if you examine more thoroughly both of the data, you will find out that in the first sample we have an extreme value ($10000) wich significantly affects the distribution of the data (positive skewness),fact that renders them unreliable.
                        As far as the second sample is concerned, we can distinguish from the graph (and from the descriptive statistics of course) that the data is normally distributed around the mean, fact that makes them more consistent to rely on and take decissions based on them, even though it has larger volatility.



                        Ιn conclusion, the real challenge of a researcher is whether he/she should exclude or not the extreme values of the sample and how he/she justify such action.






                        share|cite|improve this answer
























                          0












                          0








                          0






                          In addition to the very informative answer that Peter provided above, you should also take into serious consideration all of the descriptive statistics derived from your sample. Especially when it comes to optimum investment option selecting, skewness of your data plays crucial role in deciding which one would be the most promising in terms of profitability.



                          For instance, suppose that you have this sample: $1000,$1500,$1300,$1400,$1350,$1550,$1250,$1100,$10000,$1150,$1280. This sample implies CV=38,15% and mean profit=$2080



                          Then we have another sample:
                          $2000,$2160,$1960,$2200,-$4000,$8160,-$10000,$14160,-$15000,$19160,$2080 wich implies CV=141% and mean profit=2080



                          At first glance,whereas both of the samples have the same mean, we would opt for the first option as the optimum investment since it implies the smallest CV, but if you examine more thoroughly both of the data, you will find out that in the first sample we have an extreme value ($10000) wich significantly affects the distribution of the data (positive skewness),fact that renders them unreliable.
                          As far as the second sample is concerned, we can distinguish from the graph (and from the descriptive statistics of course) that the data is normally distributed around the mean, fact that makes them more consistent to rely on and take decissions based on them, even though it has larger volatility.



                          Ιn conclusion, the real challenge of a researcher is whether he/she should exclude or not the extreme values of the sample and how he/she justify such action.






                          share|cite|improve this answer












                          In addition to the very informative answer that Peter provided above, you should also take into serious consideration all of the descriptive statistics derived from your sample. Especially when it comes to optimum investment option selecting, skewness of your data plays crucial role in deciding which one would be the most promising in terms of profitability.



                          For instance, suppose that you have this sample: $1000,$1500,$1300,$1400,$1350,$1550,$1250,$1100,$10000,$1150,$1280. This sample implies CV=38,15% and mean profit=$2080



                          Then we have another sample:
                          $2000,$2160,$1960,$2200,-$4000,$8160,-$10000,$14160,-$15000,$19160,$2080 wich implies CV=141% and mean profit=2080



                          At first glance,whereas both of the samples have the same mean, we would opt for the first option as the optimum investment since it implies the smallest CV, but if you examine more thoroughly both of the data, you will find out that in the first sample we have an extreme value ($10000) wich significantly affects the distribution of the data (positive skewness),fact that renders them unreliable.
                          As far as the second sample is concerned, we can distinguish from the graph (and from the descriptive statistics of course) that the data is normally distributed around the mean, fact that makes them more consistent to rely on and take decissions based on them, even though it has larger volatility.



                          Ιn conclusion, the real challenge of a researcher is whether he/she should exclude or not the extreme values of the sample and how he/she justify such action.







                          share|cite|improve this answer












                          share|cite|improve this answer



                          share|cite|improve this answer










                          answered Dec 15 '18 at 23:02









                          LogicseekerLogicseeker

                          184




                          184






























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