Editing Interquartile range (section)

===Interquartile range test for normality of distribution===
The IQR, [[mean]], and [[standard deviation]] of a population ''P'' can be used in a simple test of whether or not ''P'' is [[Normal distribution|normally distributed]], or Gaussian. If ''P'' is normally distributed, then the [[standard score]] of the first quartile, ''z''<sub>1</sub>, is −0.67, and the standard score of the third quartile, ''z''<sub>3</sub>, is +0.67. Given ''mean''&nbsp;=&nbsp;<math>\bar{P}</math> and ''standard&nbsp;deviation''&nbsp;=&nbsp;σ for ''P'', if ''P'' is normally distributed, the first quartile

:<math>Q_1 = (\sigma \, z_1) + \bar{P}</math>

and the third quartile

:<math>Q_3 = (\sigma \, z_3) + \bar{P}</math>

If the actual values of the first or third quartiles differ substantially{{Clarify|date=December 2012}} from the calculated values, ''P'' is not normally distributed. However, a normal distribution can be trivially perturbed to maintain its Q1 and Q2 std. scores at 0.67 and −0.67 and not be normally distributed (so the above test would produce a false positive). A better test of normality, such as [[Q–Q plot]] would be indicated here.