Confidence Interval For Mean Calculator

Work out confidence interval for mean instantly with clear inputs, formula shown and shareable results.

About Confidence Interval For Mean Calculator

The confidence interval for a mean is x̄ ± t·s/√n, using the t distribution with n − 1 degrees of freedom because the population standard deviation is estimated from the sample.

Formula

Confidence interval

x̄ ± t(α/2, n−1) · s/√n

Worked example

With the default values below, Confidence Interval For Mean Calculator returns Margin of error of 1.941712. Change any input above and every figure here is recalculated in your browser.

Inputs used

Sample mean: 68.4
Sample standard deviationminimum 0: 5.2
Sample sizeminimum 2: 30
Confidence levelaccepts 50–99.99 %: 95 %

Results

Margin of error: 1.941712
Lower confidence bound: 66.458288
Upper confidence bound: 70.341712
Critical t value: 2.045230

Step by step

1Values used
2Confidence interval
3Margin of error= 1.941712
4Lower confidence bound= 66.458288
5Upper confidence bound= 70.341712
6Critical t value= 2.045230

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For x̄ = 68.4, s = 5.2, n = 30 at 95%?

t is about 2.0452, the standard error 0.9494, so the interval is 68.4 ± 1.942, that is 66.458 to 70.342.

Why t rather than z?

Estimating s from the sample adds uncertainty, so the t distribution has heavier tails; it approaches z as n grows.