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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. 1 SE = 8/sqrt(36)=1.3333
  2. 2 MOE = 1.96 x 1.3333 = 2.6133
  3. 3 CI = 50 plus/minus 2.6133

Confidence interval is from 47.3867 to 52.6133.

How
  1. Enter sample mean and sample standard deviation.
  2. Enter sample size and z-critical value.
  3. 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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