# Statistics for Environmental Engineers

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— =

— +

2

у

2

a

b2

Notice that each term is the square of the relative standard deviation (RSD) of the variables. The RSDs are ayly, oala, and obl b.

These results can be generalized to any combination of multiplication and division. For:

у = kabl cd

where a, b, c and d are measured and к is a constant, there is again a relationship between the squares of the relative standard deviations:

Example 10.4

X V

The sludge age of an activated sludge process is calculated from в = q X , where Xa is mixed-liquor suspended solids (mg/L), V is aeration basin volume, Qw is waste sludge flow (mgd), and Xw is waste activated sludge suspended solids concentration (mg/L). Assume V = 10 million gallons is known, and the relative standard deviations for the other variables are 4% for Xa, 5% for Xw, and 2% for Qw. The relative standard deviation of sludge age is:

= V42 + 52 + 22 = 745 = 6.7% в

The RSD of the final result is not so much different than the largest RSD used to calculate it.

This is mainly a consequence of squaring the RSDs.

Any efforts to improve the precision of the experiment need to be directed toward improving the precision of the least precise values. There is no point wasting time trying to increase the precision of the most precise values. That is not to say that small errors are unimportant. Small errors at many stages of an experiment can produce appreciable error in the final result.

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