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Standard Methods for the Examination of Water and Wastewater
المش
9221 C. Estimation of Bacterial Density
1. Precision of Fermentation Tube Test
Unless a large number of sample portions is examined, the precision of the fermentation
tube test is rather low. For example, if only 1 mL is examined in a sample containing 1 coliform
organism/mL, about 37% of 1-mL tubes may be expected to yield negative results because of
random distribution of the bacteria in the sample. When five tubes, each with 1 mL sample, are
used under these conditions, a completely negative result may be expected less than 1% of the
time.
Consequently, exercise great caution when interpreting the sanitary significance of coliform
results obtained from the use of a few tubes with each sample dilution, especially when the
number of samples from a given sampling point is limited.
2. Computing and Recording of MPN
To calculate coliform density, compute in terms of the Most Probable Number (MPN). The
MPN values, for a variety of planting series and results, are given in Table 9221:II, Table
9221:III, and Table 9221:IV. Included in these tables are the 95% confidence limits for each
MPN value determined. If the sample volumes used are those found in the tables, report the
value corresponding to the number of positive and negative results in the series as the MPN/100
Standard Methods for the Examination of Water and Wastewater
© Copyright 1999 by American Public Health Association, American Water Works Association, Water Environment Federation
mL or report as total or fecal coliform presence or absence.
The sample volumes indicated in Table 9221:II and Table 9221:III relate more specifically
to finished waters. Table 9221:IV illustrates MPN values for combinations of positive and
negative results when five 10-mL, five 1.0-mL, and five 0.1-mL volumes of samples are tested.
When the series of decimal dilutions is different from that in the table, select the MPN value
from Table 9221:IV for the combination of positive tubes and calculate according to the
following formula:
When more than three dilutions are used in a decimal series of dilutions, use the results from
only three of these in computing the MPN. To select the three dilutions to be used in determining
the MPN index, choose the highest dilution that gives positive results in all five portions tested
(no lower dilution giving any negative results) and the two next succeeding higher dilutions. Use
the results at these three volumes in computing the MPN index. In the examples given below, the
significant dilution results are shown in boldface. The number in the numerator represents
positive tubes; that in the denominator, the total tubes planted; the combination of positives
simply represents the total number of positive tubes per dilution:
Example
1
mL
0.1
mL
0.01
mL
0.001
mL
Combination
of positives
MPN Index
/100 mL
a
5/5 5/5 2/5 0/5 5-2-0 5000
b
5/5 4/5 2/5 0/5 5-4-2 2200
c
0/5 1/5 0/5 0/5 0-1-0 20
In
c, select the first three dilutions so as to include the positive result in the middle dilution.
When a case such as that shown below in line d arises, where a positive occurs in a dilution
higher than the three chosen according to the rule, incorporate it in the result for the highest
chosen dilution, as in e:
Example
1
mL
0.1
mL
0.01
mL
0.001
mL
Combination
of positives
MPN Index
/100 mL
d
5/5 3/5 1/5 1/5 5-3-2 1400
e
5/5 3/5 2/5 0/5 5-3-2 1400
Standard Methods for the Examination of Water and Wastewater
© Copyright 1999 by American Public Health Association, American Water Works Association, Water Environment Federation
Example
1
mL
0.1
mL
0.01
mL
0.001
mL
Combination
of positives
MPN Index
/100 mL
When it is desired to summarize with a single MPN value the results from a series of
samples, use the geometric mean or the median.
Table 9221:IV shows the most likely positive tube combinations. If unlikely combinations
occur with a frequency greater than 1% it is an indication that the technique is faulty or that the
statistical assumptions underlying the MPN estimate are not being fulfilled. The MPN for
combinations not appearing in the table, or for other combinations of tubes or dilutions, may be
estimated by Thomas’ simple formula:
While the MPN tables and calculations are described for use in the coliform test, they are
equally applicable to determining the MPN of any other organisms provided that suitable test
media are available.