Track 6 · Sampling and the Central Limit Theorem · Lesson 4 of 8
Standard error
Calculate the standard error of a sample mean and of a sample proportion, and explain how it differs from the standard deviation.
A report says the average commute is 37 minutes with a standard deviation of 24 minutes. Does that mean the estimate could be off by 24 minutes? No — the SD describes how much employees differ; how much the average could be off is described by the standard error, which here is only about 1.5 minutes.
The standard error (SE) of a statistic is the standard deviation of its sampling distribution: the typical distance between the statistic and the parameter it estimates, over repeated samples. It answers how precise is this estimate?
The standard deviation (SD) of the data answers a different question: how much do individuals differ from each other? Collecting more data does not make people more alike, so the SD does not shrink with . The SE does.
Included with a Formula Quest membership
It has 7 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Compute the standard error of a mean (s ÷ √n) and of a proportion (√(p̂(1 − p̂)/n))
- Explain why the SE shrinks with √n while the SD does not
- Choose SD to describe individuals and SE to describe the precision of an estimate
- Check a theoretical SE against a simulation