Equations · Probability and statistics
Standard error of the mean
How much a sample mean is expected to vary from sample to sample.
SE = σ / √n
Aethel says
S E equals sigma over the square root of n
What it says
The mean of n independent observations varies less than a single observation does: its standard deviation is the population standard deviation divided by the square root of n.
Quadrupling the sample size halves the standard error. In practice σ is estimated by the sample standard deviation.
Symbol by symbol
| Symbol | Say it | Means |
|---|---|---|
| SE | S E | the standard error of the mean |
| σ | sigma | the standard deviation of the population |
| √n | the square root of n | n is the sample size |
More onσSigma√Square root
Where you meet it
Confidence intervals, hypothesis tests and survey methods.
Questions
How do you say Standard error of the mean out loud?
SE = σ / √n is read: “S E equals sigma over the square root of n.” That is exactly what Aethel says when it meets the formula in a book.
What does SE mean in Standard error of the mean?
SE (said “S E”) is the standard error of the mean.
What does σ mean in Standard error of the mean?
σ (said “sigma”) is the standard deviation of the population.
Can I listen to the equations in my own textbook like this?
Yes. Upload a PDF, EPUB or text file and Aethel reads it aloud with every equation spoken as maths, the way it reads this one, and highlights each sentence as it goes. You can start free.