What disadvantage(s) are there of the mean deviation?
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A. B. C. D. E.E
Using absolute values can cause problems since they are difficult to work with.
The correct answer is D. All of these answers.
The mean deviation is a measure of dispersion or variability in a data set. It is calculated by taking the average of the absolute deviations from the mean. While the mean deviation has some usefulness, it also has several disadvantages, which are summarized by answer choice D.
It is based on deviations from the mean: The mean deviation calculates the average of the absolute differences between each data point and the mean. This means that it takes into account how far each observation deviates from the mean value. While this can provide information about the spread of data, it also means that the mean deviation is highly influenced by extreme values or outliers. Even a single extreme value can significantly impact the value of the mean deviation.
It is based on only two observations: This statement is not accurate. The mean deviation is based on all observations in the data set, not just two. Therefore, answer choice B is incorrect.
It uses absolute values, which are difficult to manipulate: The mean deviation requires taking the absolute values of the deviations from the mean. Absolute values are used to eliminate the positive and negative signs of the deviations, focusing only on their magnitudes. While this can simplify the calculations, it also has the disadvantage of losing the direction of the deviations. This means that the mean deviation cannot differentiate between positive and negative deviations, which can be important in some analyses.
None of these answers: This answer choice is incorrect because there are indeed disadvantages associated with the mean deviation, as explained above.
In summary, the mean deviation has limitations because it is influenced by extreme values, does not consider the direction of deviations, and uses absolute values, which may restrict certain types of analyses. Therefore, answer choice D correctly identifies all of these disadvantages.