1. What is Standard Error?

The standard error (SE) of the sample mean is a measure of how much the sample mean of the data is expected to fluctuate from the true population mean. It quantifies the precision of the sample mean as an estimate of the population mean.

2. How Does the Calculator Work?

The calculator uses the standard error formula:

Where:

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

Explanation: The standard error decreases as sample size increases, reflecting the greater precision of larger samples.

3. Importance of Standard Error

Details: Standard error is crucial for constructing confidence intervals and conducting hypothesis tests about the population mean.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

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

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

Q3: When is this formula appropriate?
A: When sampling from a normally distributed population or when sample size is large (n > 30 by Central Limit Theorem).

Q4: What if my data isn't normally distributed?
A: For small samples from non-normal populations, consider nonparametric methods or transformations.

Q5: How is SE used in confidence intervals?
A: 95% CI for population mean = sample mean ± 1.96*SE (for large samples).