The standard error of the mean measures how precisely a sample mean estimates the true mean. It is the standard deviation divided by the square root of the number of observations.
Standard error = Standard deviation ÷ √n
On the 30-day sample below: 1.28.
When to use it
It is what turns an average into an average with a margin of error. It shrinks as you collect more data, which is why more days give a firmer answer.
Worked example
Standard deviation describes how much days vary; standard error describes how sure you are about the average day. Quadrupling the number of days halves it.
=STDEV.S(C2:C31)/SQRT(COUNT(C2:C31))| Day | Website orders |
|---|---|
| 1 | 24 |
| 2 | 27 |
| 3 | 22 |
| 4 | 30 |
| 5 | 28 |
| 6 | 25 |
| 7 | 31 |
| 8 | 29 |
| 9 | 26 |
| 10 | 33 |
| 11 | 30 |
| 12 | 28 |
| 13 | 35 |
| 14 | 32 |
| 15 | 29 |
| 16 | 34 |
| 17 | 61 |
| 18 | 31 |
| 19 | 36 |
| 20 | 33 |
| 21 | 30 |
| 22 | 37 |
| 23 | 35 |
| 24 | 32 |
| 25 | 38 |
| 26 | 36 |
| 27 | 34 |
| 28 | 40 |
| 29 | 37 |
| 30 | 39 |
Common mistakes
- Do not confuse it with standard deviation; error bars drawn with one when you meant the other are very common.
- It assumes independent observations. Days in a trend or a season are not, so the real uncertainty is larger.
- Use the sample standard deviation (STDEV.S).
Calculate it yourself
Related methods
See all statistics methods or the business metrics they are used on.
Guides that use it
Further reading
Questions people ask
- What is standard error of the mean?
- The standard error of the mean measures how precisely a sample mean estimates the true mean. It is the standard deviation divided by the square root of the number of observations.
- What is the formula for standard error of the mean?
- Standard error = Standard deviation ÷ √n. On the 30-day sample data the result is 1.28.
- How do you calculate standard error of the mean in Excel?
- Use =STDEV.S(C2:C31)/SQRT(COUNT(C2:C31)) with the data in rows 2 to 31. The same formula works in Google Sheets.
About the data on this page
The figures come from a small made-up dataset, printed above in full so you can check every number by hand. Download it as daily.csv. The results are computed from those rows when the page is built, and the Excel formulas, SQL and Python on these pages are run against the same rows before publishing, so the code and the answers agree.
To get these numbers from your own data without writing formulas, try AnalyzeIt: ask in plain words and it shows the working behind every figure.
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