R summary

Matthias

The function "fivenum", defines quantiles by assuming that the i-th order 
statistic is the

         (i-0.5)/(length(x))

quantile. Thus, it defines a 25% quantile by finding the cutoff point where 
25% are below and 75% above. In this example, this is the "center" of 
27.08, counting half of this measurement as "above" and half as "below". 
This makes a lot of sense, but problem with this definition is that the min 
is not the 0% quantile, but the 1/2n-quantile.

 > (order(x)-.5)/(length(x))
  [1] 0.02272727 0.06818182 0.11363636 0.15909091 0.20454545 0.25000000
  [7] 0.29545455 0.34090909 0.38636364 0.43181818 0.47727273 0.52272727
[13] 0.56818182 0.61363636 0.65909091 0.70454545 0.75000000 0.79545455
[19] 0.84090909 0.88636364 0.93181818 0.97727273

The function "summary" is based on a definition of quantiles that is biased 
to equate the min to the 0%-quantile and max to the 100%-quantile. "The 
algorithm linearly interpolates between order statistics of x, assuming 
that the ith order statistic is the

         (i-1)/(length(x)-1)

quantile."

The solution is simple: Never use

         quantile or
         summary

if you are interested in quantiles ;-)