Mathematica and the reject SAT question..

*To*: mathgroup at smc.vnet.net*Subject*: [mg6022] Mathematica and the reject SAT question..*From*: george at mech.seas.upenn.edu ( George Jefferson )*Date*: Tue, 11 Feb 1997 01:20:12 -0500*Organization*: Mechanical Engineering*Sender*: owner-wri-mathgroup at wolfram.com

The now famous SAT question that had to be rejected boils down to this: what is the "median of the series" 1,a,a^2...a^N N is a posative even integer, a is unspecified. Seems to me, if a >=0 the median is a^(n/2) if a < 0 the median is the lowest posative member of the series: 1 if a<-1, a^n if -1<a<0. Anyway, look what mathematica does: Mathematica 2.2 for SGI Copyright 1988-94 Wolfram Research, Inc. In[1]:= <<Statistics`DescriptiveStatistics` In[2]:= Median[{1,a,a^2}] Out[2]= a In[3]:= a=-1 Out[3]= -1 In[4]:= Median[{1,a,a^2}] Out[4]= 1 In[5]:= Median[{s,q,r}] Out[5]= r It seems to work correcly for any numerical values, but always returns "something" even when it doesn't really have enough informatin..look at the last example, it seems to have ranked the elements alphabetically.. I wonder if the sat people use mathematica to check the exam..:-). ps. *they* still got it wrong even if you specify a>0 :-)