The coefficient of variation (CV) for a set of annual incomes is 18%; the coefficient of variation for the length of service with the company is 29%. What does this indicate?
Click on the arrows to vote for the correct answer
A. B. C. D. E.E
The CV is the ratio of the standard deviation to the mean, express as a percent. The higher the coefficient, the greater the dispersion.
The coefficient of variation (CV) is a measure of relative variability and is calculated by dividing the standard deviation of a dataset by its mean and then multiplying by 100. It is commonly used to compare the relative variability of different datasets.
In this question, we are given two coefficients of variation: 18% for annual incomes and 29% for the length of service with the company.
If the coefficient of variation for one dataset is higher than the coefficient of variation for another dataset, it indicates that the dataset with the higher coefficient of variation has more relative variability or dispersion compared to the other dataset.
Let's examine the answer choices:
A. More dispersion in the distribution of the incomes compared with the dispersion of their length of service: This answer suggests that the coefficient of variation for incomes (18%) is higher than the coefficient of variation for the length of service (29%). However, this contradicts the concept explained above. Therefore, this answer is incorrect.
B. Dispersions are equal: This answer suggests that the coefficients of variation for both incomes and the length of service are equal. However, this contradicts the given information. Therefore, this answer is incorrect.
C. Dispersions in the two distributions (income and service) cannot be compared using percents: This answer suggests that the coefficients of variation cannot be used to compare the relative dispersion between incomes and the length of service. However, this is not accurate. Coefficients of variation are specifically designed to compare relative variability between different datasets. Therefore, this answer is incorrect.
D. None of these answers: This option suggests that none of the provided answer choices is correct. However, we need to determine the correct answer based on the explanation provided.
E. More dispersion in the lengths of service compared with incomes: This answer correctly states that the coefficient of variation for the length of service (29%) is higher than the coefficient of variation for incomes (18%). It implies that there is more relative variability or dispersion in the lengths of service compared to the distribution of incomes. Therefore, this answer is correct.
In conclusion, the correct answer is E. More dispersion in the lengths of service compared with incomes.