No single statistical measure (mean, mode, median, extreme value, or frequency of occurrence) provides a complete summarization of a dataset, particularly in regard to its variability. Other statistical parameters are needed. Consider these two simple datasets:
Both datasets have a mean of 50 and a median of 60. But the observations in the Y dataset cluster more closely about the center than do those in the X dataset. Therefore, X’s dataset has more variability than Y’s. To obtain additional information about a dataset’s variability, we use two other measures, range and standard deviation.