1. What is Standard Error?

The Standard Error (SE) measures the precision of a sample mean as an estimate of the population mean. It quantifies how much the sample mean would vary if you repeated the study multiple times.

2. How Does the Calculator Work?

The calculator uses the Standard Error formula:

Where:

• \( s \) — Sample standard deviation
• \( n \) — Sample size

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

3. Importance of Standard Error

Details: Standard error is crucial for constructing confidence intervals and conducting hypothesis tests. It helps determine how precisely the sample mean estimates the population mean.

4. Using the Calculator

Tips: Enter the sample standard deviation (must be ≥0) and sample size (must be ≥1). The calculator will compute the standard error of the mean.

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 precision of the sample mean estimate.

Q2: Why does standard error decrease with larger sample sizes?
A: Larger samples provide more precise estimates of the population mean, reflected in smaller standard errors.

Q3: When should I use this standard error formula?
A: Use this when you have a single sample and want to estimate the precision of its mean. For proportions, use a different SE formula.

Q4: Can standard error be zero?
A: Only if there's zero variability (all values identical) or infinite sample size - both unrealistic in practice.

Q5: How is standard error used in confidence intervals?
A: 95% CI = mean ± 1.96×SE (assuming normal distribution or large sample).