Sample Proportion Calculator

Formula

To calculate the sample proportion:

\[ \hat{P} = \frac{X}{n} \]

Where:

\(\hat{P}\) is the sample proportion
\(X\) is the number of successes in the sample
\(n\) is the sample size

What is a Sample Proportion?

A sample proportion is a statistic that represents the fraction of the sample that has a particular attribute or outcome of interest. It is often used in statistics to estimate the proportion of a characteristic within a larger population. The sample proportion is a key concept in inferential statistics, where it helps to make predictions or inferences about a population based on sample data.

Example Calculation 1

Let's assume the following values:

Number of Successes (\(X\)) = 40
Sample Size (\(n\)) = 100

Using the formula:

\[ \hat{P} = \frac{40}{100} = 0.4 \]

The Sample Proportion is 0.4.

Example Calculation 2

Let's assume the following values:

Number of Successes (\(X\)) = 75
Sample Size (\(n\)) = 200

Using the formula:

\[ \hat{P} = \frac{75}{200} = 0.375 \]

The Sample Proportion is 0.375.