Averages (Arithmetic Mean) and Median - Basic Mathematics for Water and Wastewater Operators - page 110

MEDIAN
The median is defined as the value of the central item when the data are arrayed by
size. First, arrange all of the readings in either ascending or descending order, then
find the middle value.

■ Example 7.2
Problem : In our chlorine residual example, what is the median?

Solution : Arrange the values in ascending order:

0.9 0.9 1.0 1.1 1.2 1.3 1.4

The middle number is the fourth one, 1.1. So, the median chlorine residual is 1.1 mg/L.

Note: Usually the median will be a different value than the mean. If there is an
even number of values, you must add one more step, because there is no middle
value. You must find the two values in the middle, and then find the mean of those
two values.

■ Example 7.3
Problem : A water system has four wells with the following capacities: 115 gpm, 100
gpm, 125 gpm, and 90 gpm. What are the mean and the median pumping capacities?

Solution :

Mean = (115 gpm + 100 gpm + 125 gpm + 90 gpm) ÷ 4 = 107.5 gpm

To find the median, arrange the values in order:

90 gpm 100 gpm 115 gpm 125 gpm

With four values, there is no single middle value, so we must take the mean of the
two middle values:

Median = (100 gpm + 115 gpm) ÷ 2 = 107.5 gpm

At times, determining what the original numbers were like is difficult (if not
impossible) when dealing only with averages.

■ Example 7.4
Problem : A water system has four storage tanks. Three of them have a capacity of
100,000 gal each, while the fourth has a capacity of 1 million gal. What is the mean
capacity of the storage tanks?

Solution:

(100,000 + 100,000 + 100,000 + 1,000,000) ÷ 4 = 325,000 gal