#This is the page for topic 7m
     # generate the data
source("../gnrnd4.R") 
gnrnd4(1954287804,8500566)
     # be sure that we have the right data
L1
     # then, just because we know how to do it,
     # we will make a histogram of the frequencies
hist( L1, 
         main="Data from gnrnd4(1954287804,8500566)",
         xlab="Intervals across the data set",
         ylab="Frequency",
         ylim=c(0,25))
abline(h=0)
abline(h=seq(5,25,5), lty="dotted")

     # We will take a clue from the histogram and
     # decide to have intervals of width 5 starting
     # at 35 and going up to 80.  At this point
     # we will want to mimic the histogram by having
     # the intervals closed on the right.
     #
     # to do this we will set up our break points.
b_pnts <- seq( 35, 80, 5)
b_pnts
     # then we can use the cut() function to get the
     # interval into which each value in L1 falls
which_interval <- cut( L1, b_pnts)
which_interval
     # Now we have changed our problem from having
     # continuous values as in L1 to having discrete
     # values as in which_interval.  Therefore we can
     # apply the same techniques that we used for
     # the discrete case.
     #
freqs <- table( which_interval )
freqs
     # to compute the relative frequency we divide
     #  the frequencies by the total number of items
total <- length(L1)
rel_freq <- freqs/total
rel_freq
     # to compute the cumulative frequencies we 
     # use the cumsum() function
cum_count <- cumsum( freqs)
cum_count
     # to compute the cumulative relative
     # frequencies we just divide the cumulative 
     # frequencies by the total number of items
cum_rel_freq <- cum_count/total
cum_rel_freq
     # to compute the degrees to allocate in a pie
     # chart we just multiply the relative frequency
     # times 360
deg_pie <- 360*rel_freq
deg_pie

##############################
#  But we captured all that in a function so use it
###############################
#
source("../make_freq_table.R")
make_freq_table( which_interval )

####   there is one more special feature that we 
####   should see here.  We can get a nicer looking 
####   table by using the View() function

View( make_freq_table( which_interval ) )

##############################

      # Converting this new problem to an old one
      # is a good problem solving technique.  But
      # the process of conversion for this type 
      # of problem is always the same.  So, we might 
      # as well incorporate all of this into a new
      # function.  That function is collate3().
source("../collate3.R")
      #  First, see what happens if we just try to
      #  use collate3 with L1
collate3(L1)
      # The function ran but it did not give us the 
      # output we expected.  Instead it told us the 
      # lowest and highest values in the data set and
      # then made recommendations about the width of 
      # the interval. Using that information we may want
      # set the intervals to start at 35 and to have
      # a width of 5.
collate3( L1, use_low=35, use_width=5 )
      # that produced a nice frequency table, one that
      # even included a column for the midpoint of each
      # interval.

#####################
      # One feature that we did not cover was how to
      # get the intervals to be closed on the left.
      # Back at line 28 when we used the cut()
      # function we could have added the option
      # right=FALSE to force the intervals to be 
      # closed on the left.
which_interval <- cut( L1, b_pnts, right=FALSE)
which_interval
      # And, we can do the same thing with collate3
collate3( L1, use_low=35, use_width=5, right=FALSE )
      # note the change in the interval from 55 to 60.