# Standard error of proportion

In the first example of http://statisticshelp.com/confidence-interval Standard error of proportion is $$\frac{\sqrt {p(1-p)}}{n}$$

Why ?

• What do you mean? Do you want some sort of derivation of this equation? Or what? – Peter Flom Dec 1 '13 at 14:35
• @PeterFlom I know that if $X\sim N(\mu,\sigma^2)$ then $\bar X\sim N(\mu,\frac{\sigma^2}{n})$. What is the idea of the above SE for $p$? – ABC Dec 1 '13 at 14:39
• Can you write out the expression for the standard deviation of a Bernoulli variable? You should be able to work it out from the definition of standard deviation. – jbowman Dec 1 '13 at 15:14
• @jbowman i found it $$\sqrt{\frac{p(1-p)}{n}}$$ But in the linked page there isn't $\sqrt$ in the denominator(n). – ABC Dec 1 '13 at 16:11
• Ah, I see your problem! I hadn't paid enough attention to exactly what was written, my apologies. The $n$ should be included under the $\sqrt$ sign. I'm guessing, from the evident LaTeX problems on the rest of the linked page, that the author simply didn't get the formatting correct. Good catch! – jbowman Dec 1 '13 at 16:26