A sample proportion has a distribution
If a categorical data set is modelled as a random sample from a categorical population, the sample proportions must be treated as random quantities — they vary from sample to sample.
The population proportion in a category is called its probability, and is often denoted by π. The corresponding sample proportion is usually denoted by p.
Sample Statistic | Population Parameter | |
---|---|---|
Mean | ![]() |
µ |
Standard deviation | s | σ |
Proportion/probability | p | π |
In practice, we only have a single sample and must use it to get information about the underlying population.