Coefficient of variation and standard deviation are two meas

Coefficient of variation and standard deviation are two measures of dispersion or spread among data values. Provide two different sets of ten data points each as examples. Explain which of the two mentioned measures can more accurately specify which of these two data sets have more spread or variability in their data values. Calculate the standard deviation and coefficient of variation for each data set to clarify your explanation.

Solution

100% × 0 / 100 = 0%

100% × 15.138 / 102.5 = 14.77%

100% × 40.986 / 41.6 = 98.524%

The coefficient of variation is useful because the standard deviation of data must always be understood in the context of the mean of the data. In contrast, the actual value of the CV is independent of the unit in which the measurement has been taken, so it is a dimensionless number. For comparison between data sets with different units or widely different means, one should use the coefficient of variation instead of the standard deviation.