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Most probable number

Most probable number is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Most probable number rather than just read about it. In short: The most probable number method, otherwise known as the method of Poisson zeroes, is a method of getting quantitative data on concentrations of discrete items from positive/negative (incidence) data. Purpose There are many discrete entities that are easily detected but difficult to count.

Key takeaways

  • Most probable number belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Most probable number to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Most probable number from memory before moving on to harder problems.

Reference excerpt

The most probable number method, otherwise known as the method of Poisson zeroes, is a method of getting quantitative data on concentrations of discrete items from positive/negative (incidence) data.

Purpose There are many discrete entities that are easily detected but difficult to count. Any sort of amplification reaction or catalysis reaction obliterates easy quantification but allows presence to be detected very sensitively. Common examples include microorganism growth, enzyme action, or catalytic chemistry. The MPN method involves taking the original solution or sample, and subdividing it by orders of magnitude (frequently 10× or 2×), and assessing presence/absence in multiple subdivisions. The degree of dilution at which absence begins to appear indicates that the items have been diluted so much that there are many subsamples in which none appear. A suite of replicates at any given concentration allow finer resolution, to use the number of positive and negative samples to estimate the original concentration within the appropriate order of magnitude.

Applications In microbiology, the cultures are incubated and assessed by eye, bypassing tedious colony counting or expensive and tedious microscopic counts. Presumptive, confirmative and completed tests are a part of MPN. In molecular biology, a common application involves DNA templates diluted into polymerase chain reactions (PCR). Reactions only proceed when a template is present, allowing for a form of quantitative PCR, to assess the original concentration of template molecules. Another application involves diluting enzyme stocks into solution containing a chromogenic substrate, or diluting antigens into solutions for ELISA (Enzyme-Linked ImmunoSorbent Assay) or some other antibody cascade detection reaction, to measure the original concentration of the enzyme or antigen.

Weakness and importance The major weakness of MPN methods is the need for large numbers of replicates at the appropriate dilution to narrow the confidence intervals. However, it is a very important method for counts when the appropriate order of magnitude is unknown a priori and sampling is necessarily destructive.

See also Dilution assay

External links Downloadable MPN Calculator A five-replicate MPN table Details of practical implementation, but not theory US FDA article on MPN method Information on the MPN method and ballast water treatment Downloadable EXCEL program for the determination of the Most Probable Numbers (MPN), their standard deviations, confidence bounds and rarity values according to Jarvis, B., Wilrich, C., and P.-T. Wilrich: Reconsideration of the derivation of Most Probable Numbers, their standard deviations, confidence bounds and rarity values. Journal of Applied Microbiology 109 (2010), 1660 – 1667

References

Oblinger, J.L., and J. A. Koburger, J.A. (1975) "Understanding and Teaching the Most Probable Number Technique." J. Milk Food Technol. 38(9), 540–545.

Worked examples

Example 1 — a first encounter with Most probable number

Start with the simplest possible case. Write down what Most probable number claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Most probable number before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Most probable number ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Most probable number

In research
Most probable number appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Most probable number in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Most probable number is common in secondary-school and first-year university syllabi. It links to neighbouring topics Biostatistics, Laboratory techniques, Quantitative research, so understanding it makes those chapters shorter.
In everyday life
Look for Most probable number outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Most probable number in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Most probable number means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Most probable number out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Most probable number in simple terms?

The most probable number method, otherwise known as the method of Poisson zeroes, is a method of getting quantitative data on concentrations of discrete items from positive/negative (incidence) data. Purpose There are many discrete entities that are easily detected but difficult to count.

Why does Most probable number matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Most probable number?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Most probable number.

Tags

  • Biostatistics
  • Laboratory techniques
  • Quantitative research

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