Statistics for Environmental Engineers

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FIGURE 4.1 Copper data plotted on arithmetic and logarithmic scales give a different impression about the high values.

The Moving Average

Many standards for environmental quality have been written for an average of 30 consecutive days. The language is something like the following: “Average daily values for 30 consecutive days shall not exceed….” This is commonly interpreted to mean a monthly average, probably because dischargers submit monthly reports to the regulatory agencies, but one should note the great difference between the moving 30-day average and the monthly average as an effluent standard. There are only 12 monthly averages in a year of the kind that start on the first day of a month, but there are a total of 365 moving 30-day averages that can be computed. One very bad day could make a monthly average exceed the limit. This same single value is used to calculate 30 other moving averages and several of these might exceed the limit. These two statistics — the strict monthly average and the 30-day moving average — have different properties and imply different effects on the environment, although the effluent and the environment are the same.

The length of time over which a moving average is calculated can be adjusted to represent the memory of the environmental system as it responds to pollutants. This is done in ambient air pollution monitoring, for example, where a short averaging time (one hour) is used for ozone.

The moving average is the simple average of the most recent k data points, that is, the sum of the most recent k data divided by k:

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