Question

Comparing two data sets, you state in a memo to your supervisor that data set B has a comparatively larger spread or variance.

               Data set A: mean = 42.5, std deviation = 68.0, coefficient of variation = 1.6

               Data set B: mean = 28.9, std deviation = 60.7, coefficient of variation = 2.1

Your incredulous supervisor says that you must be wrong since data set A clearly has a higher standard deviation. Provide an argument supporting your contention of data set B's comparatively larger variance.

Answer 1

The coefficient of variation (CV) is the ratio of the standard deviation to the mean. Basically higher the coefficient of variation, the greater the level of dispersion around the mean. In the above case it is true that that the standard deviation, which tells the spread of the data is greater for Data A than Data B( std deviation of A  = 68.0 > std deviation > 60.7) but as we can notice its the mean of the data A is also much larger than the mean of the data B thus making the ratio of standard deviation by mean smaller which is the coefficient of variation.The smaller the CV, the more concentrated the data values are about their mean; conversely, a large CV implies that the data values are more widely dispersed about their mean value.