Gwendolyn Willett

2022-01-16

What is the formula for the standard error?

### Answer & Explanation

Andrew Reyes

$se=\sqrt{var\left(X\right)}$
Explanation:
Given a random variable X with a certain pdf f, the variance is
$var\left(X\right)=E\left({X}^{2}\right)-{E}^{2}\left(X\right)$, where E is the expected value. The standard error (or standard deviation) is just $se=\sqrt{var\left(X\right)}$. For example, if X is $N\left(\mu ,{\sigma }^{2}\right)$, the standard error is $\sigma$.

vrangett

When you are asked to find the sample error, you're probably finding the standard error. That uses the following formula: $\frac{s}{\sqrt{n}}$. You might be asked to find standard errors for other stats like the mean or proportion.