Standard Error
Standard deviation of a sample mean.
Key idea
Standard deviation of a sample mean.
In depth
The standard error of the mean is SE = σ/√n (estimated by s/√n). It measures how much the sample mean typically varies. Quadrupling the sample size halves it.
Worked example
s = 12, n = 36: SE = 12/6 = 2.
Formula
Real-world uses
- Stating how precise an average is in a scientific report or a poll
Common mistake
Mixing up the standard deviation of data with the standard error.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Standard Error?
Standard deviation of a sample mean. It is a topic at the expert level in Probability & Statistics.
What is the formula for Standard Error?
The key formula is SE = σ/√n.
Where is Standard Error used in real life?
Real-world examples: Stating how precise an average is in a scientific report or a poll.
What should I learn before Standard Error?
Make sure you are comfortable with Sampling Distributions, the previous topic in Probability & Statistics.
What is a common mistake with Standard Error?
Mixing up the standard deviation of data with the standard error.
How can I practise Standard Error?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Standard Error?
Move on to Confidence Intervals for Means next.
Related expert topics in Probability & Statistics
- Skewness and Kurtosis – Measures of asymmetry and tail heaviness.
- Residuals and R² – Error of a fit and proportion of variance explained.
- Simpson’s Paradox – A trend reverses when groups are combined.
- Law of Total Probability – Split an event over a partition.
- Bayes’ Theorem – Update beliefs with evidence.
- Medical Tests and Base Rates – Why positive results can still be probably false.