Calculate the required sample size for a given population size and margin of error.

**Required Sample Size (n):**

## Understanding Slovin's Formula

Slovin's formula is used to determine the minimum sample size required to estimate a population proportion with a given margin of error. This formula is especially useful when dealing with large populations where surveying everyone would be impractical.

### Formula

**N:**Population size**e:**Desired margin of error, expressed as a decimal (e.g., 0.05 for 5%)**n:**Sample size needed to achieve the desired precision

### Example Calculation

Suppose a researcher wants to estimate the proportion of people in a city of 10,000 residents who support a new policy, with a margin of error of 5%.

**Step 1:**Population size \( N = 10000 \)**Step 2:**Margin of error \( e = 5\% = 0.05 \)**Step 3:**Apply Slovin's formula: \[ n = \frac{10000}{1 + 10000 \cdot 0.05^2} \approx 385 \]

The researcher needs a sample size of approximately 385 to estimate the proportion with a 5% margin of error.

Suf is a senior advisor in data science with deep expertise in Natural Language Processing, Complex Networks, and Anomaly Detection. Formerly a postdoctoral research fellow, he applied advanced physics techniques to tackle real-world, data-heavy industry challenges. Before that, he was a particle physicist at the ATLAS Experiment of the Large Hadron Collider. Now, he’s focused on bringing more fun and curiosity to the world of science and research online.