Statistics for Environmental Engineers

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BODs in the 1980s are not as high as in the past. This reduction is what has improved the fishery, because the highest BODs were occurring in the summer when stream flow was minimal and water temperature was high. Several kinds of plots were needed to extract useful information from these data. This is often the case with environmental data.

Showing Statistical Variation and Precision


Measurements vary and one important function of graphs is to show the variation. There are three very different ways of showing variation: a histogram, a box plot (or box-and-whisker plot), and with error bars that represent statistics such as standard deviations, standard errors, or confidence intervals.


A histogram shows the shape of the frequency distribution and the range of values; it also gives an impression of central tendency and shows symmetry or lack of it. A box plot is a designed to convey a few primary features of a set of data. One form of box plot, the so-called box-and-whisker plot, is used in Figure 3.7 to compare the effluent quality of 12 identical trickling filter pilot plants that received the same influent and were operated in parallel for 35 weeks (Gameson, 1961). It shows the median (50th percentile) as a center bar, and the quartiles (25th and 75th percentiles) as a box. The box covers the middle 50% of the data; this 50% is called the interquartile range. Plotting the median instead of the average has this advantage: the median is not affected by the extreme values. The “whiskers” cover all but the most extreme values in the data set (the whiskers are explained in Cleveland, 1990, 1994). Extreme values beyond the whiskers are plotted as individual points. If the data come from a normal distribution, the fraction of observations expected to lie beyond the whiskers is slightly more than 1%. The simplicity of the plot makes a convenient comparison of the performance of the 12 replicate filters.

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