Statistical concepts and applications

¶ … median, and the mode. The mean is impacted by data points that are far out in the distribution. The further out on the tail that outlier data points are, the more the mean will be pulled in that direction (toward the tail extremes). This results in a mean that does not represent the majority of the data points (the central tendency) very well. The median represents the point at which half of the data points fall below a certain point and half of the data points fall above that point. The mode is useful for distributions that are nominal (the mean and the median do not apply to nominal data) and to distributions that are bi-modal.

Central tendency is one of the most useful descriptive statistic measures because of it functions as a general purpose "snap-shot" of distribution. The human mind looks for patterns in data, and central tendency measures cater to that aspect of human understanding by providing labels for data sets that represent patterns. Using central tendency measures permits researchers to employ a common language and specific methods to derive at the data labels that are collectively known as measures of central tendency.

Variability is an important measure of distributions because it reflects the spread of the data. Distribution variability is fundamentally a measure of distance, and the terms for describing this distance include standard deviation, range, and inter-quartile range. The range refers to the entire distribution but the inter-quartile range refers to the center two of four quartiles. Standard deviation refers to the standard distance of particular data points from the mean.

A combination of measures of central tendency and measures of variability can be used to construct a generalized visual display of the data points in a distribution. A standard deviation is so "standardized" that, generally speaking, 70% of the data points will fall within one standard deviation, and 90% of the data points will fall within two standard deviations. Standard deviation is one of the most common ways for researchers to describe data as it forms a basis for comparing data from study to study.