Using the Confidence Interval Calculator
Holding everything else constant, a larger sample narrows the interval and a higher confidence level widens it. That tradeoff reflects the precision and coverage built into the method.
Worked example
Use the example inputs below to reproduce this result. These are the form's starting values, not recommended targets. Changing your inputs updates your result above; this worked example stays fixed for comparison. Results are rounded for display.
Example inputs
- Sample mean
- 50
- Sample standard deviation
- 10
- Sample size
- 100
- Confidence level
- 95%
Example result
- Lower bound
- 48.040036
- Upper bound
- 51.959964
- Margin of error
- 1.959964
Method and assumptions
Mean ± z × standard deviation / √n. Normal approximation, not a small-sample Student t interval.
Check what the data represents
A statistical result is only meaningful in relation to the observations and assumptions behind it. Keep track of whether values describe a whole population or a sample, whether observations are independent, and which distribution the method uses. More decimal places cannot compensate for a sample that does not represent the question you are trying to answer.
Common question
Does 95% confidence mean a 95% probability that this particular interval contains the mean?
In the usual frequentist interpretation, the method covers the true mean in 95% of repeated samples under its assumptions. The confidence level describes that procedure, not a probability assigned to the fixed mean after observing one interval.
Guide updated .