Sample Proportion

A basic inferential building block for confidence intervals and hypothesis tests about a population share.

Sample proportion % = successes ÷ sample size × 100.

Tip: Keep “Successes” and “Sample Size (n)” on the same basis (period, units, and population) before calculating Sample Proportion.

Cluster: Statistics hub · Percentage error · Percentage guide

Sample proportion is the percent of successes (or events) in a sample.

Enter number of successes and sample size n.

Count of successes/events
Total observations

Sample Proportion

Understanding Sample Proportion

How we calculate. Sample proportion % = successes ÷ sample size × 100. The form uses the same arithmetic as the worked examples on this page. See our methodology and accuracy policy.

Real-world scenario: A typical Sample Proportion case uses successes 42 and sample size (n) 200. Enter the same figures below to reproduce the worked path.

What is Sample Proportion?

A basic inferential building block for confidence intervals and hypothesis tests about a population share.

  • Successes ≤ n
  • Define success clearly
  • Use with MoE for interval width

The Formula

Sample Proportion
p̂ % = (Successes ÷ n) × 100

Worked Example

Scenario: 42 successes in a sample of 200.
Step 1: 42 ÷ 200 = 0.21
Step 2: × 100 = 21%
Answer: Sample proportion is 21%.

Common Use Cases

  • Surveys: yes-rate estimates
  • A/B tests: conversion shares
  • QA sampling: defect shares

Pro Tips

  • Report n with the percent
  • Check independence assumptions
  • Small n → unstable p̂

Limitations: Sample Proportion results are educational statistics aids—not formal statistical certification. Confirm assumptions (SRS, large-sample approximations, labeling) for your analysis.

FAQ

Is this the population proportion?

No—this is the sample estimate p̂. Population p is usually unknown.

What if n is 0?

Proportion is undefined—enter a positive sample size.

Authoritative References

For statistical definitions and survey practice, consult:

  • NIST ITL — measurement and statistical guidance
  • AAPOR — survey response-rate standards
  • NCHS — public health statistics context