Sampling Distributions
Distribution of a statistic across samples.
Key idea
Distribution of a statistic across samples.
In depth
A sampling distribution describes how a statistic (like the mean) varies from sample to sample. Its spread is much smaller than that of individual observations, and it is what allows us to quantify uncertainty.
Worked example
Taking many samples of size 25 and recording each mean builds the sampling distribution of x̄.
Real-world uses
- Understanding how much a sample average can vary from the true population average
Common mistake
Confusing the distribution of the data with that of the statistic.
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 Sampling Distributions?
Distribution of a statistic across samples. It is a topic at the expert level in Probability & Statistics.
Where is Sampling Distributions used in real life?
Real-world examples: Understanding how much a sample average can vary from the true population average.
What should I learn before Sampling Distributions?
Make sure you are comfortable with Central Limit Theorem, the previous topic in Probability & Statistics.
What is a common mistake with Sampling Distributions?
Confusing the distribution of the data with that of the statistic.
How can I practise Sampling Distributions?
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 Sampling Distributions?
Move on to Standard Error 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.