Statistics for Environmental Engineers

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6.5, 9.2, 7.4, 6.3, 5.6, 7.3, 8.3, 7.2, 7.5, 6.1, 9.4, 5.4, 7.6, 8.1, and 7.9 mg/L.


The population is all specimens having a known concentration of 8.0 mg/L. The sample is the 27 observations (measurements). The sample size is n = 27. The random variable is the measured concentration in each specimen having a known concentration of 8.0 mg/L. Experimental error has caused the observed values to vary about the true value of 8.0 mg/L. The errors are 6.9 — 8.0 = -1.1, 7.8 — 8.0 = — 0.2, + 0.9, — 2.8, — 0.3, +1.6, + 0.7, and so on.

Plotting the Data


A useful first step is to plot the data. Figure 2.1 shows the data from Example 2.1 plotted in time order of observation, with a dot diagram plotted on the right-hand side. Dots are stacked to indicate frequency.


A dot diagram starts to get crowded when there are more than about 20 observations. For a large number of points (a large sample size), it is convenient to group the dots into intervals and represent a group with a bar, as shown in Figure 2.2. This plot shows the empirical (realized) distribution of the data. Plots of this kind are usually called histograms, but the more suggestive name of data density plot has been suggested (Watts, 1991).


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Order of Observation


FIGURE 2.1 Time plot and dot diagram (right-hand side) of the nitrate data in Example 2.1.

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