# Here is the object we created last time. It contains a variable
# named "Peabody." 
> ls()
[1] "PeabodyFrame"

# If we "attach" the data frame, we can refer to Peabody directly
# rather than extracting it using PeabodyFrame$Peabody (which would,
# for example, lead to a pretty weird histogram title).

> attach(PeabodyFrame)
> Peabody
 [1]  69  72  94  64  80  77  96  86  89  69  92  71  81  90  84  76 100  57  61
[20]  84  81  65  87  92  89  79  91  65  91  81  86  85  95  93  83  76  84  90
[39]  95  67

# Here's the stem-and-leaf plot we did last time:

> stem(Peabody)

  The decimal point is 1 digit(s) to the right of the |

   5 | 7
   6 | 14
   6 | 55799
   7 | 12
   7 | 6679
   8 | 01113444
   8 | 566799
   9 | 00112234
   9 | 556
  10 | 0


# R can do histograms, but there are some problems with the default
# settings. It tends to produce square plots. It chooses poor breakpoints
# and labels the edges of the histobars rather than the midpoints. It also
# leaves the histogram hanging in mid air.

> hist(Peabody)

# We can force a more horizontal aspect ratio; we want the figure to be
# about 2/3 as tall as it is wide. Here, "pin" stands for "plot inches,"
# se we are telling R that we want a figure that is 6 inches wide and
# 4 inches tall. (We may need to drag the edge of the plot window in order
# to fit everything.)

> par(pin=c(6,4))

# The aspect ratio is improved, but the other problems remain:

> hist(Peabody)

# A look at the help page for the histogram function shows us that there's
# a parameter called "breaks" that determines the breakpoints.

> help(hist)
starting httpd help server ... done

# Here, we explicitly list the breakpoints we want:

> hist(Peabody, breaks=c(54.5,59.5,64.5,69.5,74.5,79.5,84.5,89.5,94.5,99.5,104.5))

# We can actually do that with less typing by telling R we want them
# to be a sequence from 54.5 to 104.5 in steps of 5:

> hist(Peabody, breaks=seq(54.5,104.5,5))

# But the X-axis label is still hanging in mid-air, and the midpoints
# of the intervals are not labeled. We can take control of the axis
# by supressing them altogether...

> hist(Peabody, breaks=seq(54.5,104.5,5),axes=FALSE)

# ...and then adding them where we want them. Here, side=1 refers to the
# bottom horizontal side.

> axis(side=1, at=seq(57,102,5))

# That's better, except that the axis label is still hanging in mid-air.
# If we specify "pos=0" R will draw the axis line at Y=0, which is where
# we actually want it:

> hist(Peabody, breaks=seq(54.5,104.5,5),axes=FALSE)
> axis(side=1, at=seq(57,102,5), pos=0)

# Now we add the left vertical axis:

> axis(side=2,at=seq(0,8,2))

# Finally, we give the whole histogram a line to sit on:

> abline(h=0)

# We can specify a different title from the default:

> hist(Peabody, breaks=seq(54.5,104.5,5),axes=FALSE, main="Histogram of Peabody Picture Vocabulary Scores")

# If we make the title too long, it won't fit:

> hist(Peabody, breaks=seq(54.5,104.5,5),axes=FALSE, main="Histogram of Peabody Picture Vocabulary Scores of 40 10-year-olds in Oakland, California")

# But we can make it fit by adding a line feed (look for the "\n" roughly half way through the title):

> hist(Peabody, breaks=seq(54.5,104.5,5),axes=FALSE, main="Histogram of Peabody Picture Vocabulary Scores\nof 40 10-year-olds in Oakland, California")
> axis(side=1, at=seq(57,102,5), pos=0)
> axis(side=2,at=seq(0,8,2))
> abline(h=0)

# Now THAT'S a nice histogram!


# We reviewed calculation of the mean and median:
 
> mean(Peabody)
[1] 81.675
> median(Peabody)
[1] 84

# The 17th case has the value 100. Let's suppose that someone accidentally
# entered that as 1000:

> Peabody
 [1]  69  72  94  64  80  77  96  86  89  69  92  71  81  90  84  76 100  57  61
[20]  84  81  65  87  92  89  79  91  65  91  81  86  85  95  93  83  76  84  90
[39]  95  67
> Peabody[17] <- 1000
> Peabody
 [1]   69   72   94   64   80   77   96   86   89   69   92   71   81   90   84
[16]   76 1000   57   61   84   81   65   87   92   89   79   91   65   91   81
[31]   86   85   95   93   83   76   84   90   95   67

# The mean is highly affected by the bad data point:

> mean(Peabody)
[1] 104.175

# But the median is unchanged:

> median(Peabody)
[1] 84
> Peabody[17] <- 100
> mean(Peabody)
[1] 81.675
 
# That illustrates the principle of "resistance" that can help us choose
# a measure of central tendency. The median is said to be resistant to the
# effects of extreme data or skewed distributions.