Central Tendency and Dispersion

The most commonly required characterisation of any sample size of measurements is a statistic representing a value that usually occurs commonly, and in the centre part of the range of observations. The arithmeticmean is most important, but other important central values will be described. Conversely, the second most useful statistic describes the degree to which observations are scattered. Variance,the square of standard deviation, is the most powerful descriptor of dispersion. The following summary explains these concepts in earth-science contexts. Descriptive measures like mean and variance may be calculated for any sample of measurements, without any theoretical knowledge of the population from which the sample is drawn. However, the nature of the populations may affect their usefulness. In this chapter, through Chapter 4, it is important to note that we deal with observations that are scalars, measurements encapsulated in a single quantity. Quantities like 2.1 m, 4 kg, and dimensionless values like 0.03 and 7% are scalars.