For a standard normal random variable z (mean = 0, stddev=1), the range [_0.6745,0.6745] will contain the value of z half the time.
In other word, the quartiles for such a random variable are _0.6745, 0, 0.6745, and the IQR is about 1.35. Henry Rich Devon McCormick wrote: > The reason I started looking at this was upon reading about using the IQR > (inter-quartile range)* 1.35 or so as a robust alternative to standard > deviation as a measure of dispersion for approximately normal distributions: > I was wondering about the derivation of the magic number "1.35". > > On Fri, Oct 16, 2009 at 8:15 PM, Don Guinn <[email protected]> wrote: > >> That's why you need to be careful with median and quartiles. You must know >> how it is calculated before you interpret the result. >> >> On Fri, Oct 16, 2009 at 6:38 PM, Sherlock, Ric <[email protected] >>> wrote: >>> The following is based on Keith Similie's stats companion. >>> >>> NB. Median and quartiles >>> midpt=: -:@<:@# >>> median=: -:@(+/)@((<.,>.)@midpt { /:~) >>> Q1=: [: median ] #~ median > ] >>> Q3=: [: median ] #~ median < ] >>> quartiles=: Q1 , median , Q3 >>> >>> Another definition of median where the domain is integers. >>> >>> median=: ~.@((<.,>.)@midpt { /:~) >> ... >> ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
