Skip to content

Confidence interval calculator

The margin of error and range for a sample mean at 80% to 99.9% confidence.

Favorite

Results

Confidence interval 69.783–74.217

How it works

x̄ ± z × s ÷ √n

A confidence interval gives a range that likely contains the true average of the whole population. The margin of error is the z-value for your confidence level times the standard error (s ÷ √n). Quadrupling the sample size halves the margin. This uses the normal (z) distribution, which is accurate for samples of about 30 or more; smaller samples need the slightly wider t-distribution.

  1. s ÷ √n 8 ÷ √50 = 1.1314
  2. z × standard error 1.959964 × 1.1314 = 2.2174
  3. Mean ± margin 72 ± 2.2174 = 69.783–74.217

Printed from rocketcalc.io/math/confidence-interval