Table 3.

Some advantages of the new standard normal (from Stigler, 1983) [10]

Density	$f\left(x\right)={\mathrm{e}}^{-\pi x^2}$	$f\left(x\right)=\frac{1}{\sqrt{2\pi }}{\mathrm{e}}^{-\frac{x^2}{2}}$
f(0)	1	$\frac{1}{\sqrt{2\pi }}=0.39894$
Quartile (approx.)	$\frac{1}{4}$	0.675
Mean deviation	$\frac{1}{\pi }$	$\frac{\sqrt{2}}{\pi }$
Standard deviation of the sample median	$\frac{1}{2}$	$\sqrt{\frac{\pi }{2}}$