# Statistics for Environmental Engineers

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The graph is illustrated in Figure 3.1 for a time series of 36 hourly observations (time, in hours, is measured from left to right).

 30 27 41 38 44 29 43 21 15 33 33 28 49 16 22 17 17 23 27 32 47 71 46 42 34 34 34 44 27 32 28 25 36 22 29 24

0    10    20    30

Time

FIGURE 3.1 Digidot plot shows the sequence and distribution of the data.

FIGURE 3.2 Multiple two-variable scatterplots of wastewater treatment plant data.

As each observation arrives, it is placed as a dot on the time-sequence plot and simultaneously recorded with its final digit on a stem-and-leaf plot. For example, the first observation was 30. The last digit, a zero, is written in the “bin” between the tick marks for 30 and 35. As time goes on, this bin also accumulates the last digits of observations having the values of 30, 33, 33, 32, 34, 34, 34, and 32. The analyst thus generates a complete visual record of the data: a display of the data distribution, a display of the data time history, and a complete numerical record for later detailed arithmetic analysis.

### Scatterplots

It has been estimated that 75% of the graphs used in science are scatterplots (Tufte, 1983). Simple scatterplots are often made before any other data analysis is considered. The insights gained may lead to more elegant and informative graphs, or suggest a promising model. Linear or nonlinear relations are easily seen, and so are outliers or other aberrations in the data.

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