A phycologist is interested in determining the proportion of algae samples from a local rivulet that belonged to a particular phylum. A random sample of 50 alga was obtained and each alga was categorized as either being cyanobacteria or not. It was found that 38 were, in fact, cyanobacteria. The proportion 'p-hat' that were cyanobacteria is

The proportion of cyanobacteria is the relationship between the whole sample and the actual quantity of cyanobacteria found in the sample, that were not other algae. In general, proportions are written as fractions. The numerator is the number of cyanobacteria in the sample, while the denominator is the total number of organisms in the sample.

So, in the exposed example we know that

The sample was composed of 50 algae
There were two categories for the sample: algae that were cyanobacteria, and algae that were not cyanobacteria
Algae that were cyanobacteria = 38
Algae that were not cyanobacteria = 12

If we want to study the relationship between the sample and cyanobacteria and express it as a proportion, then we need to divide the number of cyanobacteria by the number of algae in the sample. This is

38/50 ----> Fraction expression of the relationship between cyanobacteria

and the sample

0.76 ----> Proportion of cyanobacteria in the whole sample.