The correct answer is: A. The measure of skewness is dependent upon the amount of dispersion.
A measure of skewness is a way of describing the shape of a distribution. It tells us whether the distribution is symmetrical, skewed to the left, or skewed to the right. The amount of dispersion is a measure of how spread out the data are. A distribution with a lot of dispersion has data points that are spread out over a wide range of values. A distribution with little dispersion has data points that are clustered close together.
The measure of skewness is not dependent upon the amount of dispersion. A distribution can be skewed even if the data points are clustered close together. For example, the following distribution is skewed to the right, even though the data points are clustered close together:
The mean, median, and mode are all measures of central tendency. The mean is the average of the data points. The median is the middle value in the data set. The mode is the most frequent value in the data set.
In a symmetric distribution, the mean, median, and mode are all the same. In a positively skewed distribution, the mean is greater than the median and the mode. In a negatively skewed distribution, the mean is less than the median and the mode.
The following diagram shows the relationship between the mean, median, and mode in a symmetric, positively skewed, and negatively skewed distribution:
Therefore, the statement “The measure of skewness is dependent upon the amount of dispersion” is not true.