Environmental Engineering Reference
In-Depth Information
7
Averages (Arithmetic
Mean) and Median
Whether we speak of harmonic mean, geometric mean, or arithmetic mean, each is
designed to find the “center” or “middle” of a set of numbers. These terms capture
the intuitive notion of a “central tendency” that may be present in the data. In sta-
tistical analysis, an “average of data” is a number that indicates the middle of the
distribution of data values. The three most important measures of the center used in
statistics are the
mean
,
median
, and
mode
. In this chapter, we discuss the first two.
AVERAGES
An average is a way of representing several different measurements as a single num-
ber. Although averages can be useful by indicating about how much or how many,
they can also be misleading, as we demonstrate below. You find two kinds of aver-
ages in waterworks/wastewater treatment calculations: the
arithmetic mean
(or sim-
ply
mean
) and the
median.
Definition:
The
mean
(what we usually refer to as an average) is the total of values
of a set of observations divided by the number of observations. We simply add
up all of the individual measurements and divide by the total number of measure-
ments we took.
■
Example 7.1
Problem:
The operator of a waterworks or wastewater treatment plant takes a chlo-
rine residual measurement every day; part of this operating log is shown below. Find
the mean.
Day
Chlorine Residual (mg/L)
Monday
0.9
Tuesday
1.0
Wednesday
0.9
Thursday
1.3
Friday
1.1
Saturday
1.4
Sunday
1.2
Solution:
Add up the seven chlorine residual readings: 0.9 + 1.0 + 0.9 + 1.3 + 1.1
+ 1.4 + 1.2 = 7.8. Next, divide by the number of measurements: 7.8 ÷ 7 = 1.11. The
mean chlorine residual for the week was 1.11 mg/L.
109
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