Confidence Interval Calculator
Confidence interval calculator
Compute confidence interval from mean, sd, sample size, and z-critical.
InputsStatistics4 fieldsLive
Result
[47.38666667, 52.61333333]
Margin of error = 2.61333333.
Live update
interval estimate
Margin vs SD
Sample size signal
Advanced options
Formula
CI = mean plus/minus z x (sd / sqrt(n)) Symbol legend
| Symbol | Meaning | Unit | Copy |
|---|---|---|---|
\bar{x} | Sample mean | data unit | |
z | Critical z value | standard score | |
s | Sample standard deviation | data unit | |
n | Sample size | count |
- Compute standard error as sd divided by square root of n.
- Multiply standard error by z-critical to get margin of error.
- Add and subtract margin around mean for lower and upper bounds.
Example
Worked example: mean 50, sd 8, n 36, z 1.96
- 1 SE = 8/sqrt(36)=1.3333
- 2 MOE = 1.96 x 1.3333 = 2.6133
- 3 CI = 50 plus/minus 2.6133
Confidence interval is from 47.3867 to 52.6133.
How
- Enter sample mean and sample standard deviation.
- Enter sample size and z-critical value.
- Read margin of error and interval bounds.
Avoid
- Using variance instead of standard deviation.
- Entering non-integer sample size.
- Using wrong critical value for chosen confidence level.
FAQ
Does this use z-based interval only?
Yes, this implementation uses a provided z-critical value.
Can I change confidence level?
Yes, change z-critical according to your desired confidence level.
What is margin of error here?
It is z multiplied by standard error of the mean.
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