Sampling Distribution of the Sample Proportion Calculator
Enter a population proportion and a sample size to find the mean and standard error of the sampling distribution of the sample proportion.
What this calculator does
The sampling distribution of the sample proportion describes how a proportion (p-hat) calculated from repeated random samples of size n would vary around the true population proportion p, if you drew many such samples.
The formula
The mean of the sampling distribution equals the population proportion, p. Its standard error is calculated as the square root of p(1-p) divided by n: SE = sqrt(p(1-p)/n). A smaller standard error means sample proportions cluster more tightly around the true value, which happens as sample size grows.
Normal approximation rule of thumb
Statisticians commonly treat the sampling distribution as approximately normal when both n*p and n*(1-p) are at least 10. This calculator flags whether that condition is met for your inputs (1 means the condition holds, 0 means it does not).
Note: this tool is for general educational and planning purposes and does not replace formal statistical training or software.