A 95% confidence interval for a mean is a range, mean ± margin, built so that the method captures the true mean 95% of the time. The margin is a t-value times the standard error.
95% CI = Mean ± t(0.975, n − 1) × Standard deviation ÷ √n
On the 30-day sample below: 2.61.
When to use it
An average without a range invites over-reading. "32 orders a day, give or take 3" is much more useful than "32 orders a day".
Worked example
The figure here is the margin (the ± part) for average daily website orders. Add it to and subtract it from the mean to get the interval.
=CONFIDENCE.T(0.05,STDEV.S(C2:C31),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
- It is about the average, not individual days. Most days fall outside the confidence interval for the mean, and that is expected.
- It assumes independent observations and a roughly normal sample mean, which 30 days usually give, but not with heavy trends or seasonality.
- CONFIDENCE.NORM uses the normal distribution; CONFIDENCE.T uses t, which is right for samples of this size.
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 confidence interval for a mean?
- A 95% confidence interval for a mean is a range, mean ± margin, built so that the method captures the true mean 95% of the time. The margin is a t-value times the standard error.
- What is the formula for confidence interval for a mean?
- 95% CI = Mean ± t(0.975, n − 1) × Standard deviation ÷ √n. On the 30-day sample data the result is 2.61.
- How do you calculate confidence interval for a mean in Excel?
- Use =CONFIDENCE.T(0.05,STDEV.S(C2:C31),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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