Appendix D

Volumes 1-3
January 1993

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Calculation of most probable numbers (MPN)

Table I shows the most probable numbers of coliforms per 100 ml or g of test material corresponding to the number of gas-positive tubes in the coliform test.

Table I has been adapted from a conversion table prepared for the analysis of drinking waters where 10, 1.0 and 0.1 ml of the water under test are used as test portions. When other sized portions of the test material are placed in the tubes, MPN values obtained from Table II must be multiplied by an appropriate number, to correct for the actual amount of test material in the tubes, and also to obtain the MPN per g (ml) as is usually done for foods, rather than per 100 ml (g), for which the values are given in the table. The volume of diluent added to the tubes (and which accompanies the test material) is ignored when calculating the MPN.

Example:

The quantities in each of the five tubes of the three dilution series represent 1, 0.1 and 0.01 g (ml), respectively of the test material. According to Table I, a reading of 5-1-0 gives a value of 33 when 10, 1 and 0.1 g (ml) respectively are used. However, since only 1/10 of these amounts were actually used in the analysis, the value of 33 obtained from Table II must be multiplied by 10 giving 33 x 10 = 330 organisms per 100 g (ml) of test material. If the results need to be expressed per g (ml), the MPN value is 330 ÷ 100 = 3.3. When higher dilutions are used, the same procedure is followed, but the multiplier (dilution factor) is enlarged to relate the amount of test material actually present to the values given for 10, 1.0 and 0.1 g (ml) in Table I.

Dilution factor = Reciprocal of the dilution of the analytical unit.

For calculating the MPN, use the dilution factor of the middle set of the three dilutions selected.

To determine which consecutive dilutions to use, refer to the combinations shown below: (See also Table III).

1. If only 3 dilutions are made, use the results for those 3 dilutions to compute the MPN. Examples a and b, Table II.
2. If more than 3 dilutions are employed, use the results of only 3 consecutive dilutions. Select the highest dilution (last dilution, i.e. dilution with the smallest quantity of product), in which all 5 tubes are positive and 2 subsequent higher dilutions. Examples c and d, Table II.
3. If more than 3 dilutions are made, but none of the dilutions tested have all 5 tubes positive, use the first 3 dilutions. Example e, Table II.
4. If a positive tube occurs in the dilution higher than the 3 chosen to rule, the number of such positive tubes should be added to those of the next lower dilution. Example f, Table II.
5. If the tubes of all sets of a dilution series are positive, choose the 3 highest dilutions of the series and indicate by a "greater than" symbol (>) that the MPN is greater than the one calculated. Example g, Table II.

Example g, Table II.

Refer to Table II and look up the value which corresponds to the number of positive tubes obtained.

MPN/100 ml

=

No. microorganisms (Table I)

x

dilution factor of middle set of tubes