Enter the population standard deviation, confidence level, and desired margin of error to calculate the required sample size to estimate a population mean.

**Required Sample Size:**

## Understanding Sample Size Calculation for Mean

This calculator uses the following formula to determine the sample size required to estimate a population mean within a specified margin of error and confidence level:

where:

- \( n \) = Sample size
- \( Z \) = Z-score associated with the confidence level
- \( \sigma \) = Population standard deviation
- \( E \) = Margin of error

### Real-Life Example: Estimating Average Time Spent on a Website

Suppose a company wants to estimate the average time users spend on their website, with a 95% confidence level and a margin of error of 5 minutes. Based on previous data, they estimate the population standard deviation is 10 minutes.

Here’s the step-by-step calculation:

**Step 1:**Set the values: confidence level = 95%, margin of error = 5, standard deviation (σ) = 10.**Step 2:**Find the Z-score for a 95% confidence level (Z ≈ 1.96).**Step 3:**Use the formula:$$ n = \frac{{(1.96)^2 \cdot (10)^2}}{{(5)^2}} = 15.37 $$**Interpretation:**The company would need a sample size of at least 16 people to estimate the average time within a 5-minute 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.