To calculate the coefficient of variation (CV), we use the formula:
CV = (Standard Deviation / Mean) * 100
For the given population with a standard deviation of 4.5 and a mean of 60:
CV1 = (4.5 / 60) * 100 = 7.5
For the refit population with a standard deviation of 5.2 and a mean of 75:
CV2 = (5.2 / 75) * 100 = 6.93
Now, let's comment on the results:
The coefficient of variation (CV) measures the relative variability between the mean and standard deviation of a dataset. It is commonly used to compare the variability of different datasets, especially when the means and standard deviations are on different scales.
In this case, the coefficient of variation for the given population (CV1 = 7.5) is higher than that of the refit population (CV2 = 6.93). This implies that the variability, relative to the mean, is higher in the given population.
Additionally, since the CV is expressed as a percentage, we can compare the magnitudes of the coefficients of variation. A higher value indicates a greater variability relative to the mean. Therefore, the given population exhibits a higher relative variability than the refit population.