Editing Mode (statistics) (section)

===Van Zwet condition===

Van Zwet derived an inequality which provides sufficient conditions for this inequality to hold.<ref name=vanZwet1979>{{cite journal | last1 = van Zwet | first1 = WR | year = 1979 | title = Mean, median, mode II | journal = Statistica Neerlandica | volume = 33 | issue = 1| pages = 1–5 | doi=10.1111/j.1467-9574.1979.tb00657.x}}</ref> The inequality

:Mode ≤ Median ≤ Mean

holds if

:F( Median - {{mvar|x}} ) + F( Median + {{mvar|x}} ) ≥ 1

for all {{mvar|x}} where F() is the [[cumulative distribution function]] of the distribution.