1. What is Standard Error?

The Standard Error (SE) measures the accuracy with which a sample represents a population. It quantifies the variability of the sample mean from the population mean in a normal distribution.

2. How Does the Calculator Work?

The calculator uses the Standard Error formula:

Where:

• \( \sigma \) — Population standard deviation
• \( n \) — Sample size

Explanation: The formula shows that standard error decreases as sample size increases, and increases with greater population variability.

3. Importance of Standard Error

Details: Standard Error is crucial for constructing confidence intervals and conducting hypothesis tests. It helps determine how far the sample mean might be from the true population mean.

4. Using the Calculator

Tips: Enter the population standard deviation (σ) and sample size (n). Both values must be positive numbers (n must be at least 1).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between standard deviation and standard error?
A: Standard deviation measures variability in the data, while standard error measures the precision of the sample mean estimate.

Q2: When should I use this calculator?
A: Use it when you need to calculate the standard error of the mean for normally distributed data.

Q3: What if my data isn't normally distributed?
A: For non-normal distributions, other methods like bootstrapping might be more appropriate.

Q4: How does sample size affect standard error?
A: Standard error decreases as sample size increases, following the square root law (SE ∝ 1/√n).

Q5: Can I use sample standard deviation instead of population σ?
A: For large samples, sample standard deviation can approximate σ, but for small samples, consider using t-distribution.