#This is a script showing a number of examples of making 
#    box and whisker plots in R.  We will use the same 
#    data that we used for the histograms.

    # we want to generate the data in the given table
source("../gnrnd4.R")
gnrnd4(1497539102, 78301453)
     # as usual, verify that we have the right values
head( L1 )   # by default this shows us the first 6 values
tail( L1 )   # by default this shows us the last 6 values
     #  then to make a box plot we just use the
     #  boxplot() function
boxplot( L1 )
     # That plot came out in a vertical format. Let us 
     # switch that to a horizontal format
boxplot( L1, horizontal = TRUE)

     #  That is enough for the requirements of this course
     #  but as we have seen before, it might be nice to 
     #  fix this up a bit.

     # Caution:  because the default orientation is 
     #   vertical, to change the scale in this horizontal
     #   orientation we will use the ylim parameter.

boxplot( L1, horizontal = TRUE, ylim=c(140,240),
      main="Data from the first table on the background sheet.",
      xlab = "data values given in table 1"
      )   
abline(v=seq(140,240,10), lty="dotted", col="darkgray")
     # That made it easier to get approximate values. 

     # And do this once more with a finer scale
     # and with even more info

     #  first use summary to get the values highlighted
     #  in the box plot
s_hold <- summary(L1)
     #  Then create a bottom label
b_lab <- paste("min=", s_hold[1], "   Q1=", s_hold[2],
               "   Med=",s_hold[3], "   Q3=",
               s_hold[5], "   max=", s_hold[6])

boxplot( L1, horizontal = TRUE, ylim=c(140,240),
         main="Data from the first table on the background sheet.",
         xlab =b_lab,
         xaxp=c(140,240,20) )
abline(v=seq(140,240,5), lty="dotted", col="darkgray")

#   
#    Now look at table 2
#

gnrnd4(723859503, 7800145)
L1
boxplot(L1, horizontal=TRUE)
    #  or, again, we can fix this up

s_hold <- summary(L1)
#  Then create a bottom label
b_lab <- paste("min=", s_hold[1], "   Q1=", s_hold[2],
               "   Med=",s_hold[3], "   Q3=",
               s_hold[5], "   max=", s_hold[6])

boxplot( L1, horizontal = TRUE, ylim=c(140,240),
         main="Data from the second table on the background sheet.",
         xlab =b_lab,
         xaxp=c(140,240,20) )
abline(v=seq(140,240,5), lty="dotted", col="darkgray")
#   
#    Now look at table 3
#

gnrnd4(1849829701, 79001403)
L1
boxplot(  L1, horizontal = TRUE)
#  or, again, we can fix this up

s_hold <- summary(L1)
#  Then create a bottom label
b_lab <- paste("min=", s_hold[1], "   Q1=", s_hold[2],
               "   Med=",s_hold[3], "   Q3=",
               s_hold[5], "   max=", s_hold[6])

boxplot( L1, horizontal = TRUE, ylim=c(140,220),
         main="Data from the third table on the background sheet.",
         xlab =b_lab,
         xaxp=c(140,220,20) )
abline(v=seq(140,220,5), lty="dotted", col="darkgray")

#   
#    Now look at table 4
#

gnrnd4(1849829704, 18001800)
L1
boxplot(L1, horizontal=TRUE)
#  or, again, we can fix this up

s_hold <- summary(L1)
#  Then create a bottom label
b_lab <- paste("min=", s_hold[1], "   Q1=", s_hold[2],
               "   Med=",s_hold[3], "   Q3=",
               s_hold[5], "   max=", s_hold[6])

boxplot( L1, horizontal = TRUE, ylim=c(140,220),
         main="Data from the fourth table on the background sheet.",
         xlab =b_lab,
         xaxp=c(140,220,16) )
abline(v=seq(140,220,5), lty="dotted", col="darkgray")
#
#    A few more steps may help us see how close this is
#    to a normal distribution.  If it is normal then we 
#    expect about 25% of the values to be less than the
#    mean - 0.675*sd and about 25% of the values to be
#    greater than mean + 0.675*sd, and the mean and 
#    median should be about the same.  Let us find and 
#    graph those three values
source("../pop_sd.R")
sd_hold = pop_sd( L1 )
mu <- mean( L1 )
low_val <- mu - 0.675*sd_hold
high_val <- mu + 0.675*sd_hold
abline( v=c(low_val, mu, high_val),
        col="red", lty="dashed")
#   
#    Now look at table 5
#
     # this time we are using gnrnd5 so load that 
     # function into our environment
source("../gnrnd5.R")
gnrnd5(143879025405, 124001500, 134002100)
head(L1)
tail(L1)
boxplot(L1, horizontal = TRUE)
#  or, again, we can fix this up

s_hold <- summary(L1)
#  Then create a bottom label
b_lab <- paste("min=", s_hold[1], "   Q1=", s_hold[2],
               "   Med=",s_hold[3], "   Q3=",
               s_hold[5], "   max=", s_hold[6])

boxplot( L1, horizontal = TRUE, ylim=c(100,260),
         main="Data from the fifth table on the background sheet.",
         xlab =b_lab,
         xaxp=c(100,260,16) )
abline(v=seq(100,260,10), lty="dotted", col="darkgray")