# script for topic 7p
#
     #  to work with percentiles we need a significantly 
     #  large set of values.
source("../gnrnd5.R")
gnrnd5(41583023104, 31000444)
L1
L2 <- sort(L1)
L2
     # to find the 41st percentile, find the index  
     # that is at 0.41*(number of items in the data)
0.41*232
     # then look round up and look at that item
L2[ 96 ]
     # to find the 95th percentile, find the index  
     # that is at 0.95*(number of items in the data)
0.95*232
     # then look round up and look at that item
L2[ 221 ]
     # to find the 43rd percentile, find the index  
     # that is at 0.43*(number of items in the data)
0.43*232
     # then look round up and look at that item
L2[ 100 ]  
     # R provides a function to get percentiles from our 
     # data, without even sorting the data.  This is the 
     # quantile function.
     # Re-do the problems
quantile(L1, 0.41)
quantile(L1, 0.95)
quantile(L1, 0.43)  # this gives us a different answer
     # let us see if we can get some info on this
?quantile
     # and we can give quantile() a whole list of
     # percentiles to find
quantile( L1, c(0.20, 0.33, 0.14, 0.78))
     # or even a sequence of values
quantile( L1, seq(0.60,0.95,0.05))


     # If we want to know what percentile is the value
     # 487 we find 487 in the sorted data and then get
     # its position
which( L2==487)
     # then find the percent that index is of the
     # total size of the data and then round down,
     # but we never go over 99%
213/232*100
     #