Sampling Distribution of Proportion Calculator

Uncover the secrets of sample proportions! Calculate the mean and standard deviation of the sampling distribution, and visualize it in an interactive graph.

Calculate Sampling Distribution of Proportion

Population Proportion (p):

Sample Size (n):

Results:

Mean of the Sampling Distribution (μ_p̂):

Formula: $\mu_{\hat{p}} = p$

Standard Deviation (Standard Error) (σ_p̂):

Formula: $\sigma_{\hat{p}} = \sqrt{\frac{p(1-p)}{n}}$

Visualization:

Understanding Sampling Distribution of Proportion

The sampling distribution of the proportion is the probability distribution of sample proportions ($\hat{p}$) from all possible random samples of the same size ($n$) drawn from a population with a true proportion ($p$).

Population Proportion (p): This is the proportion of individuals in the entire population that possess a specific characteristic you are interested in.

Sample Size (n): The number of individuals you include in your sample from the population.

Mean of the Sampling Distribution ($\mu_{\hat{p}}$): The mean of the sampling distribution of $\hat{p}$ is equal to the population proportion ($p$).

Standard Deviation (Standard Error) of the Sampling Distribution ($\sigma_{\hat{p}}$): This measures the variability of the sample proportions and is calculated as $\sqrt{\frac{p(1-p)}{n}}$. It's also known as the standard error of the proportion.

This calculator helps you quickly determine these key measures and visualize the distribution, aiding in understanding how sample proportions vary around the true population proportion.