What happens to standard deviation when sample size increases?
Understand the Problem
The question is asking about the relationship between sample size and standard deviation, specifically how standard deviation behaves when the sample size increases.
Answer
The standard deviation of the distribution of sample means decreases.
The final answer is that the standard deviation of the distribution of sample means decreases when the sample size increases.
Answer for screen readers
The final answer is that the standard deviation of the distribution of sample means decreases when the sample size increases.
More Information
As the sample size increases, the standard deviation of the sample means decreases due to the Law of Large Numbers, which ensures more precise estimates of the population mean.
Tips
Do not confuse the standard deviation of the sample (which estimates the population's standard deviation) with the standard deviation of the sample means (which decreases with larger samples).
Sources
- University of Texas Health Science Center - uth.tmc.edu
- Central Limit Theorem - Statistics LibreTexts - stats.libretexts.org
- Physics Forums - physicsforums.com
