Central Limit Theorem Calculator
Find the mean and standard error of the sampling distribution of the mean for a sample size.
Change the values and press Calculate to work out your own figures.
Enter the population mean, standard deviation and sample size.
Show the working
- μ(x̄) = μ = 70
- σ(x̄) = σ ÷ √n = 12 ÷ √36 = 2
How to use it
Enter the population mean, standard deviation and sample size.
Probabilities can be typed as decimals, fractions or percentages. Show the working gives the formula with your numbers in it.
Key facts
μx̄ = μ; σx̄ = σ ÷ √n
Why it matters
Whatever the shape of the population, the means of large enough samples are approximately normally distributed, which is what makes confidence intervals and t-tests work. n ≥ 30 is a common rule of thumb.
Questions
What is the standard error for σ = 12, n = 36?
2.
Does the population need to be normal?
No, for large enough samples.
Formulas
μx̄ = μ; σx̄ = σ ÷ √n
Sources
Limitations
- Probabilities can be typed as decimals (0.25), fractions (1/4) or percentages (25%).