Statistics for Environmental Engineers

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Simple plots help reveal the sample’s distribution. Some of these plots have already been discussed in Chapters 2 and 3. Dot diagrams are particularly useful. These simple plots have been overlooked and underused. Environmental engineering references are likely to advise, by example if not by explicit advice, the construction of a probability plot (also known as the cumulative frequency plot). Probability plots can be useful. Their construction and interpretation and the ways in which such plots can be misused will be discussed.

Case Study: Industrial Waste Survey Data Analysis


The BOD (5-day) data given in Table 5.1 were obtained from an industrial wastewater survey (U.S. EPA, 1973). There are 99 observations, each measured on a 4-hr composite sample, giving six observations daily for 16 days, plus three observations on the 17th day. The survey was undertaken to estimate the average BOD and to estimate the concentration that is exceeded some small fraction of the time (for example, 10%). This information is needed to design a treatment process. The pattern of variation also needs to be seen because it will influence the feasibility of using an equalization process to reduce the variation in BOD loading. The data may have other interesting properties, so the data presentation should be complete, clear, and not open to misinterpretation.

Dot Diagrams


Figure 5.1 is a time series plot of the data. The concentration fluctuates rapidly with more or less equal variation above and below the average, which is 687 mg/L. The range is from 207 to 1185 mg/L. The BOD may change by 1000 mg/L from one sampling interval to the next. It is not clear whether the ups and downs are random or are part of some cyclic pattern. There is little else to be seen from this plot.

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