Formula
The margin is the z multiplier times the standard deviation, divided by the square root of the sample size:
Interval = mean ± z × standard deviation / √sample size
1.96 is the usual multiplier for about 95% when the standard deviation is known. This page does not look up a t table.
Assumptions
- You supply the z multiplier.
- The standard deviation is greater than zero.
Worked example
Mean 50, standard deviation 10, 25 observations, and z of 1.96 give 46.08 to 53.92.
Input definitions
- Z multiplier
- The number of standard errors on each side. 1.96 is the example.
- Sample size
- How many observations are in the mean.
Limitations
This uses a z multiplier, not a t critical value. It is not a medical or survey conclusion.
Questions
Why is 1.96 filled in?
It is a common 95% multiplier when the deviation is treated as known. You can type another multiplier.
Does a larger sample narrow the interval?
Yes. The margin divides by the square root of the sample size.