Statistical Applications for Environmental Analysis and Risk Assessment

Chapter SixBasic Statistical Measures: Descriptive or Summary Statistics

6.1 Introduction And Overview

As Indicated In Chapter 5, a graphical review of the data is always a recommended first step in data analysis. Based on the results of the graphical analysis, the appropriate descriptive statistics such as the mean or median, standard deviation, skewness, and percentiles are computed to summarize the data and for use in subsequent statistical analyses. The mean is a measure of the center of the data, while the standard deviation provides a sense of the dispersion or spread of the data relative to the mean. The larger the standard deviation of the data, the less informative is the mean, because such data might contain values in the tails of the distribution that are very different from the mean. The normal distribution, which is a commonly assumed probability distribution for data, has the interesting property that approximately 68%, 95.5%, and 99.7% of the values in a normal distribution fall within one, two, and three standard deviations, respectively, on either side of the mean. Whereas skewness is typically caused by the presence of a few unusually large (right-skew) or unusually small (left-skew) values in the data, the data distribution can be described as heavy-tailed if there are more values in the tails (extremes) than would be present in the normal distribution.

The presence of unusual data values, often referred to as outliers, creates problems in the computation ...