Questions About Variability

Abstract

The word variability is vague and requires precise definition in a statistical context. In a sample, the simplest measurement of variability is the range,i.e. the difference between the largest and smallest values. This statistic has limited application because it is strongly dependent on sample size, ignores much information in the data and is highly sensitive to odd values in the data. More appealing are contrasts among percentiles, the most widely used being the interquartile range (Section 1.3.8) which has the useful property that it is the spread of the middle fifty percent of sample members. Other percentiles may also have a place in the definition of variability, a point touched upon in Section 1.3.10. Sample variance and standard deviation are widely used statistics to describe variability in a sample. Their interpretive value is limited to circumstances in which the Normal distribution can be regarded as a reasonable approximation to the underlying frequency or probability distribution, a point considered further in Section 19.1.2.