How to use the confidence interval for a mean calculator
Find a confidence interval for a mean using the normal approximation. Enter sample mean, standard deviation, sample size, confidence level in the fields above; the standard error, critical z, margin of error, lower bound, upper bound are computed instantly and plotted on the chart so you can see how the answer changes.
Formula
Variables
- m — Sample mean
- s — Standard deviation
- n — Sample size
- cl — Confidence level (%)
Worked example
With sample mean = 50, standard deviation = 8, sample size = 64, confidence level = 95 %, the calculator gives standard error ≈ 1; critical z ≈ 1.959964; margin of error ≈ 1.959964; lower bound ≈ 48.04004; upper bound ≈ 51.95996.
Frequently asked questions
What is the formula for the confidence interval for a mean calculation?
Standard error = s / √(n). Critical z = norminv(0.5+cl / 200). Margin of error = [Critical z] × [Standard error]. Lower bound = m-[Margin of error]. Upper bound = m+[Margin of error]. Here m is sample mean, s is standard deviation, n is sample size, cl is confidence level (%).
What inputs do I need for the confidence interval for a mean calculator?
You need sample mean, standard deviation, sample size, confidence level in %. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use this calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.