#This is a further look at measures of central tendency

     #  We want to generate the values in the given tables.
     #  First, we should bring the gnrnd4 program into our 
     #       environment.
source("../gnrnd4.R")
     #  then we can generate the values
gnrnd4(1845678904, 12800649)
     #  now, print out the values so that we can check to be 
     #  sure that we have generated the correct values
L1
     #  Then, we can find the mean and median of the data
mean( L1 )
median(L1)
     #   There is something that we want to notice about the 
     #   mean and the median.  If we change a value in the list
     #   to be an extreme value, that is far different from the 
     #   rest of the values, a real outlier, then we will change 
     #   mean by a lot bit we will not change teh median much at all.

     #   We will change the 77.8 that is the 16th value in the 
     #   list to be 778 (perhaps it was just a typing error where
     #   we dropped the decimal point).
L1[ 16 ] <- 778
     #   Let us look at L1 again to see that change
L1
     # now look at the mean and median and see how much they changed
mean( L1 )
median(L1)

     #  Then, we will look at a different aspect of the mean.
     #  In particular, if we have a large set of data, then
     #  it is really hard to change the mean by a lot just by
     #  adding more values at the upper or lower ends to the existing
     #  data

     #  First we will load the gnrnd5 function.
source("../gnrnd5.R")
     #  Then we will generate a large collection of data
gnrnd5( 177083055604, 345005678)
     #  That generated 557 values, lets look at the 
     #  first 10 and then at the last 8
head( L1, 10 )
tail( L1, 8 )
     # now look at the mean
mean( L1 )
     # now, add 10 values, all down in the 450 to 500 range
     #  first, combine the 10 new values in a variable called L2
L2 <- c( 456, 487, 476, 459, 497, 481, 463, 482, 477, 489)
     #  just as a point of interest, find the mean of 
     #  these new values
mean(L2)  # this is really different from the mean of the L1 values
     #  then combine L1 and L2 to make L3
L3 <- c( L1, L2 )
     # note, in the environment area, that L3 now has 567 values
     # find the mean of L3
mean( L3 )  # see how different it is from the 568.1034  mean of L1