The standard deviation of given population is 4.5 with a mean of 60 and the refit population has a standard deviation of 5.2 with a mean of 75. Calculate the coefficient of variation for both populations and comment on the results.
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.
To calculate the coefficient of variation, you need the formula:
Coefficient of Variation (CV) = (Standard Deviation / Mean) * 100
Let's compute the coefficient of variation for both populations.
For the given population:
Standard Deviation = 4.5
Mean = 60
CV of given population = (4.5 / 60) * 100 = 7.5
For the refit population:
Standard Deviation = 5.2
Mean = 75
CV of refit population = (5.2 / 75) * 100 = 6.93
Now, let's analyze the results:
1. Given Population: The coefficient of variation is 7.5%. This means that the standard deviation is 7.5% of the mean. A higher coefficient of variation indicates higher variability in the data. Therefore, the given population has relatively higher variability compared to its mean.
2. Refit Population: The coefficient of variation is 6.93%. This indicates that the standard deviation is 6.93% of the mean. Similarly, a higher coefficient of variation suggests more variability. Therefore, the refit population also has relatively higher variability compared to its mean.
Comparing the results, we see that both populations have higher variability in their data compared to their respective means. However, the given population has a slightly higher coefficient of variation (7.5%) than the refit population (6.93%), indicating slightly more variability in the given population.