# This is a series of commands that we will use in class.
# It seems that this could be more efficient than having everyone
#   type the commands themselves.
# I will try to document the process as we go along

################################### Bar Plot ########
# First we will look at bar plots
#  If we know the height that we want for each bar then
#  we can just create a vairable to hold the heights
# and then generate the plot

how_high <- c(4.3, 5.2, 7.6, 2.4, 8.9, 3.1)
barplot( how_high )
#
# there are a few things we could do to improve that 
# plot.  We could, for example, give each value a name.
names( how_high ) <- c("Ford","Chevy","Dodge",
                       "BMW", "Honda","Volvo")
# and then plot the variable again
barplot( how_high )
#
# And we could change the command to include some 
#  titles, perhaps chage the vertical scale, and add
#  some color
barplot( how_high, main="Our First Bar Plot",
         xlab="My various automobiles", 
         ylim=c(0,10), col=rainbow(6),
         ylab="miles driven (x10000)")
# 
# And then we could add some horizontal grid lines
abline(h=0)
abline(h=seq(from=2, to=10, by=2),
       col="darkgreen", lty="dotted")

# A different use of the bar plot is to show the frequency
# of a relatively small set of values. For example, we will
# load the gnrnd4 program into our environment and then 
# generate and look at some values.

source("../gnrnd4.R")
gnrnd4( 700275302, 800031)
L1

# just looking at the values we can see that there are 
# only a few different values.  We can use the   
#    table()   function to get the frequency of each

table( L1 )

# that is nice, but a graph would be better
barplot( table(L1) )

# and, again, we could make that fancier by adding more
# commands
barplot( table(L1), main="Frequency distribution of grades",
         col=rainbow(9), xlab="Points out of 40 on test 1",
         ylab="Frequency", ylim=c(0,14))
abline(h=0)
abline(h=seq(2,14,2), col="darkgrey", 
       lty="dotted")

############################### Histogram ##############

# we would want to make a histogram of data that covers 
# wider range of values.  That is because we are less 
# interested in seeing the frequency of each value than we
# are in seeing the frequency of values within "bins"

#
# First we will generate some new values

gnrnd4(1457267703,32200456)
L1

# It is hard to even begin to see how those values
# are distributed but with a simple   hist()
# command we can get a good picture of this

hist( L1 )

# notice that R has made many arbitrary choices for 
# us in order to divide up the span of values.  One
# choice is the number of "bins", another is the 
# width of each "bin".
# 
# Having seen the values like this we might want to 
# change some of the choices.  For example, by using 
#   summary()   command we can find the minimum and 
# maximum values.

summary(L1)

# now that we know we have values from 48.10 to 77.6
# we could decide to make our "bins" cover the values
# from 48 to 78 and to do that in 6 steps, each 5
# long.  The new histogram command would be

hist( L1, xlim=c(48,78),xaxp=c(48,78,6),
      breaks=seq(48,78,5), xlab="My bins",
      ylim=c(0,25), yaxp=c(0,25,5),
      main="My Version of the Histogram")
#
# and we can make it easier to read with some 
# grid lines
abline(h=seq(5,25,5), col="darkgray", lty="dotted")
# You might note that R does not care if you use
# gray or grey.

# One of the important things to recognize in
# the histogram is whether the "bins" are 
# "closed" on the left or on the right.  In our
# example, by default, the bins are closed on the
# right.  With our data and breaks we will see a 
# small change if we close the bins on the left.

hist( L1, xlim=c(48,78),xaxp=c(48,78,6),
      breaks=seq(48,78,5), right=FALSE,
      ylim=c(0,25), yaxp=c(0,25,5),
      main="My Version of the Histogram",
      xlab="Bins now closed on left")
abline(h=seq(2,14,2), col="darkgrey", 
       lty="dotted")

#
###################### box and Whisker Plot ########
#
# Box and Whisker plots show us the relative 
# poisition of the quartiles.  Again, we need
# some data to use here.

gnrnd4( 376299509, 153035421374)
L1
# and then, leading into looking at a box and
# whisker plot, let us find the quartiles
summary( L1 )
#and now look at the plot
boxplot( L1 )
#
# the defaut box plot is vertical
# We can make it horizontal by a simple change
boxplot( L1, horizontal=TRUE)

# in either case, the rectangle identifies the 
# relative positon of the first and third 
# quartile points, with the heavy line in the middle
# of the rectangle showing the position of the 
# median, i.e., the second quartile point.
# In both of these plots the whiskers extend to
# the min and max values, Q0 and Q4.

#
# One special feature of the box and whisker plots
# is that the whiskers will not extend beyond 
# 1.5*IQR below Q1 or above Q3.
# We can see tht with different data, a new summary,
# and a new plot.

gnrnd4( 217849309, 340805354374)
L1
summary( L1 )

boxplot( L1, horizontal=TRUE)

# from the summary we see that the IQR is 
# 540.0-494.5 or 45.5.  That means that 1.5*IQR is
# 1.5*45.5 = 68.25.  Q1-68.25 is 426.25 while
# Q3+68.25 = 608.25.  However, if we look at the
# sorted data values
head( sort(L1) )
tail( sort(L1) )
# We see that we have 1 value, namely 392, that is 
# lower than our lower limit of 426.25 nd one 
# value that is higher than our upper limit 
# of 608.25, namely, 610.  These two extreme 
# values are "outliers".  The boxplot extends 
# whiskers as far as the lowest value not lower
# than Q1-(1.5*IQR) and to the hghest value
# not higher than Q3+(1.5*IQR).

# We could augment our boxplot to show those 
# limits.
abline( v=c(426.25,608.25), col="red")
abline(v=seq(400,600,50), lty="dotted",
       col="darkblue")
#
###################### pie chart ########
#
# Understanding that you really do not want to 
# use pie charts, it is still possible to make 
# in R.  We just need to have the relative 
# values in each of the pieces.  For slices to
# represent the values 23, 19, 37, 15, and 32,
# we could do the following.
chunk <- c( 23, 19, 37, 15, 32)
pie( chunk )
# or, a slightly more colorful
pie( chunk, col=rainbow(5))
# we will not look any further into pie charts.

#
###################### dot plot ########
#
# The dot plot was a great tool for us when we 
# did not have computers.  It was a simple method
# that allowed a person to really build up a
# bar chart by just reading and ploting successive
# data points.  

# As noted in the web pages, there is no built-in
# command to do a dot plot in R.  However, we do
# have a function that would do it for us.  

# We will start with some new data
gnrnd4(257686204,400035)
L1
# note that these are values that show a lot of
# repetition.  
#  We will load our function 
#  (be sure to note the underscore)

source("../dot_plot.R")
dot_plot( L1 )
# 
# Really, this is no better than using or barplot
barplot(table(L1))

#
#
###################### stem and leaf ########
#
# this was another old technique that was useful
# before we had computers.  It allowed us to 
# build a histogram, and sort the datavalues,
# in a two step process.  However, in most cases,
# the "bins" of the histogram would have to 
# correspond to groups of ten values.  Thus, for 
# the data
gnrnd4( 780124504, 1100065)
L1
# we need to load our function
source("../stem_leaf.R")
stem_leaf( L1 )
#getting a result that translates into  having the
# data be 40, 41, 43, 46, 46, 46, 47, 
#         50, 51, 53, 54, 55, 57, 58, 58, 58, 59,
# and so on.
#
#####################  scatter plot ########3
#
# here we have pairs of data values that we want 
# to graph on and xy-plot
# For example, we could generate the data
gnrnd4(1569811106, 3120070405, 32000150 )
# this produces vlaues in both L1 and L2
L1
L2
# We really have pairs of data values so that
# we want to be looking at the points
# (44.6, 35.7), (32.4, 25.8), (42.0, 36.7),
# (44.4, 36.9), and so on.
# We plot these points just as we did back in 
# algebra class.  The command to do this in R
# is the plot() function.
plot( L1, L2 )
# 
# as usual we can override the defaults to create
# a possibly more appropriate graph.  For example, 
# just the few changes shown here may help
plot( L1, L2, xlim=c(-5,50),
      ylim=c(-5,50), xaxp=c(-5,50,11),
      yaxp=c(-5,50,11),xlab="x values",
      ylab="y values", main="My scatter plot")

abline(h=seq(-5,50,5),v=seq(-5,50,5),
       col="darkgreen", lty="dotted")
abline(h=0, v=0 )

#
##################### make a frequency table #########
#
# let us create some data where we have a 
# few discrete values that are repeated some 
# different numbers of times
gnrnd4( 600878701, 900023)
L1
# we know how t find the frequency of each value
# by using the table command
table( L1 )
# However, we want to have a complete frequency
# table that extend that result by including the 
# relative frequency, the cumulative frequency,
# the relative cumulative frequency, and even
# the number of degrees for each slice of a 
# pie chart.  The web page on this walks us
# through a tedious process to reach that goal.
# Then it gives us a function to do all of the
# work at once.  We will load and use that
# function.

source("../make_freq_table.R")
make_freq_table( L1 )
# The output from that function, when used that 
# way, is shown in the console pane.  An 
# alternative is to do something like
mft <- make_freq_table( L1 )
# Which displays nothing of the results.
# However, we can then use the command View(),
# with a capital V, to see the results in 
# a special form of the editor pane.
View( mft )
#
# That special display has certain advantages over
# the console display.  We can demonstrate
# some of thse in class.

#
####################  Grouping Data #########
#
# There are times when the data, especially 
# continuous data, makes more sense if we can
# arrange it into groups ("bins", "buckets",
# "intervals", etc.) as is the case for the 
# following data

gnrnd4(1573289104, 23101650 )
L1
# looking at the summary we can find the range
summary( L1 )
#
# We have already seen R group the data when 
# we looked at a histogram of the data
hist( L1 )
# in my run of that R created intervals 10 wide
# running from 110 to 220.
#
# Can we do the same thing and then, for those
# intervals, create a frequency table similar 
# to the one we saw above for discrete data?
# The web page walks us through a long process
# to do this, but it ends with a function,
# collate3(), that will do this for us.
#
# Load collate3
source("../collate3.R")
#
# We will take a two phase process to make 
# our "bins" and produce our frequency table.
#
# First, a simple run of collate3()
collate3( L1 )
#
# The console output from that gives us the min 
# and max values, and it suggests a width.
# In this case, in order to mimic the 
# histogram, we will set the starting value
# for the first "bin" to be 110 and the 
# width of the "bin" to be 10.
#
collate3( L1, use_low=110, use_width=10 )
# This produces the frequency table in the
# console pane. We can get abetter looking
# table in the editor by assigning the result
# of collate3() to a variable and then View
# that variable.

grp <- collate3( L1, use_low=110,
                 use_width=10)
View( grp )

# Just as we saw in the histogram discussion, 
# we do need to be aware of which side of the
# intervals is the "closed" side.  In the 
# default case, above, that was the right end.
# A simple change in the command will change
# this to be closed on the left end.  This
# may change the resulting table.
grp_left <- collate3( L1, use_low=110,
                 use_width=10, right=FALSE)
View( grp_left )

#
############### Getting approximate measures
############### from grouped data
#
# It is unfortunate, but sometimes when we get
# data it it already grouped in a sort of 
# frequency table.  For example, look at the
# following table
#
#      Interval   Frequency
#      (55, 63]       7
#      (63, 71]       9
#      (71, 79]       3
#      (79, 87]      15
#      (87, 95]      18
#      (95, 103]      6
#
# Our challenge is to find the approximate mean,
# standard deviation, and variance for this 
# data.  We can do this by finding the midpoints
# of each interval.  In this case the first 
# midpoint is (55+63)/2 = 59. Then the midpoints
# just increase by 8 for each subsequent interval.
# We can get such a list of values via

mpnts <- seq( from=59, to=103, by=8)
mpnts

# Then we put the frequencies in a variable

freqs <- c( 7, 9, 3, 15, 18, 6)
freqs

# and now we can create a new variable that
# holds each midpoint the the same number of 
# times as the frequency for its interval

x <- rep( mpnts, freqs )
x

# and then our approximations are done on that
# variable

mean(x)
sd(x) #assuming we are looking at a sample
sd(x)^2  #variance of a sample
# or, if we had a population
source("../pop_sd.R")
pop_sd( x )  # standard deviation of a population
pop_sd( x )^2  #variance of a population

#
############### Percentiles ####
#
# There are two kinds of questions to answer.
# 1. For a given set of values, 
#          find the 93rd percentile?
# 2. For a given set of values,
#         what is the percentile of a specific
#         value?
#
# Here is a set of values
gnrnd4( 389568304, 5100532)
L1
# to look at percentiles we need to ort the 
# values
L1_sorted <- sort(L1)
L1_sorted
# we can find the length of the list
length(L1_sorted)
# then, the 93rd percentile will be the value
# that has 93% of the values less than it in
# the sorted list
0.93*length(L1_sorted)
# that answer is 78.12, so the 79th value
# has 93% of the values less than it
L1_sorted[ 79 ]

# the value 564 is in the list, what is its
# percentile? We can find the position of 564
# in the sorted list.

which( L1_sorted == 564)
#
# It is position 64
# Therefore its percentile is 64/length(L1_sorted)
64/length(L1_sorted)*100
# and then round down to get 76%