The Mean, Median and Mode are the three widely used (and misused) measures of the data's center. Each measure has its own purpose for describing the dataset. Refer to Lind, Ch 3, pp. 57-60, 62-65, 66-68 (Note: Chart 3-4 has mean and mode labels switched.)
For these variables, almost all random variables correspond to the measures of tendency.
However, in B5 it should be noted that the measures of central tendency are far from each other. In fact, there exist two modes for the variable. Also since the mean and the median are calculated and are not in the sample, the chance of picking a random variable which is the same as these two measures is zero.
If the data is significantly skewed, the mean becomes an inappropriate measure of central tendency. It should be noted that the mean will be more likely to be found on the dataset where the skewness can be found. For example, a data set which ranges from 7-40 which is positively skewed can have a mean which is 15 only because most of the data range from 7-18 for instance. The presence of outliers which are extremely low or high data can also adversely affect the effectiveness of the mean as a measure of central tendency.
If data is significantly skewed, the mode becomes the best approximation of the data's center. Mean cannot be relied upon because of the presence of outliers while median can also be misleading. Thus, mode which represents the most number of variable can be best represent the data's center at this situation.
If the data is significantly skewed, the range will not be affected. ...