As such, the population proportion can be defined as follows: P = X N {\displaystyle P={\frac {X}{N}}} where X {\displaystyle X} is the count of successes in the population and N {\displaystyle N} is the size of the population. This mathematical definition can be generalized to provide the definition for the sample proportion: p ^ = x n {\displaystyle {\hat {p}}={\frac {x}{n}}} where x {\displaystyle x} is the count of successes in the sample and n {\displaystyle n} is the size of the sample obtained from the population.