Population proportion

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Population proportion

In statistics, the term population proportion refers to the fraction of the total population that possesses a certain characteristic. It is a measure used to describe the relative size of a subset within a population. The population proportion is often denoted by the symbol p.

Calculation

The population proportion is calculated by dividing the number of individuals in the subset of interest by the total number of individuals in the population. Mathematically, it is expressed as:

$p=\frac{X}{N}$

where:

• X is the number of individuals in the subset.
• N is the total number of individuals in the population.

Example

Suppose a survey is conducted to determine the proportion of people in a city who prefer a certain brand of coffee. If 200 out of 1,000 surveyed individuals prefer the brand, the population proportion is:

$p=\frac{200}{1000}=0.2$

This means that 20% of the population prefers the brand of coffee.

Importance in Statistics

The population proportion is a fundamental concept in inferential statistics. It is used in various statistical analyses, including the construction of confidence intervals and the performance of hypothesis testing. Understanding the population proportion helps in making inferences about the entire population based on a sample.

Related Concepts

• Sample proportion
• Confidence interval
• Hypothesis testing
• Binomial distribution
• Central limit theorem

See Also

• Statistics
• Population
• Sample (statistics)
• Parameter (statistics)

Related Pages

• Sample proportion
• Confidence interval
• Hypothesis testing
• Binomial distribution
• Central limit theorem

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