g01arf
g01arf
© Numerical Algorithms Group, 2002.
Purpose
G01ARF Constructs a stem and leaf plot
Synopsis
[plot,lines,sorty,unit,ifail] = g01arf(prt,y<,nstepx,nstepy,unit,range,ldp,...
ifail>)
Description
G01ARF produces a stem and leaf display for a single sample of n
observations. The stem and leaf display shows data values
seperated into the form of a 'stem' and a 'leaf'. For example, a
value of 473 could be represented as 47 3 where the stem is 47
and the leaf is 3. The data is scaled using a value known as the
'leaf digit unit'. In the above example the leaf digit unit would
be 1.0.
The following example illustrates a stem and leaf display.
For the 10 observations:
1.8 2.3 2.1 1.9 2.1 2.4 2.0 2.0 1.9 2.1
the stem and leaf display is:
1 1 8
3 1 99
5 2 00
5 2 111
2 2
2 2 3
1 2 4
where the leaf digit unit is 0.1 so that 1 8 represents 1.8
(i.e., 18*0.1). The leaf digit unit distinguishes between the
numbers 18.0, 1.8, 0.18 etc which may otherwise all be
represented by 1 8.
Included in the above display is an initial column specifying the
cumulative count of values, up to and including that particular
line, from either the top or bottom of the display, whichever is
smaller. An exception to this is when the line on which the
median lies is reached, in which case the actual count of values
on that line is displayed, rather than a cumulative count, and
this is highlighted by enclosing the count in parentheses. In
this case the median is 2.05 and thus falls between the two lines
at which the cumulative count has reached n/2 where n is the
number of observations.
Some of the other features of the stem and leaf display are
illustrated by the following two examples;.
For the 30 observations:
-19.0 -3.0 -1.0 0.0 1.0 2.0 2.0 3.0 3.0 3.0
4.0 4.0 4.0 4.0 4.0 5.0 5.0 5.0 5.0 6.0
6.0 6.0 7.0 7.0 8.0 10.0 11.0 11.0 13.0 31.0
the stem and leaf display may be:
1 1. 9
1 1*
1 -0.
3 -0* 13
15 +0* 012233344444
15 +0. 55556667788
5 1* 011
2 1. 3
1 2
1 2.
1 3 1
In the above display all the data are plotted and the leaf digit
unit is 1.0. Also in this display different leaves, that is
different digits, may be plotted on a particular line. In this
case we have 5 possible digits per line, that is 2 lines per
stem, and these are represented as follows;
* : indicates that the line may contain the digits 0 to 4
. : indicates that the line may contain the digits 5 to 9
Alternatively the stem and leaf display may look like:
LO -19
2 -0* 3
3 +0T 1
5 +0* 01
10 +0T 22333
(9) +0F 444445555
11 +0* 66677
6 +0T 8
5 1* 011
2 1T 3
HI 31 1
Again the leaf digit unit is 1.0 but in this display just the
1
data between the fences, which are the hinges +-1 -* the inter-
2
hinge range, are plotted. Any data points that fall outside the
fences are presented separately in the display under the headings
LO for those points below the lower fence and HI for those points
above the upper fence.
Again in this display different leaves, that is different digits,
may be plotted on a particular line. However in this case we have
2 possible digits per line, that is 5 lines per stem, and these
are represented as follows;
* : indicates that the line may contain the digits 0 or 1
T : indicates that the line may contain the digits 2 or 3
F : indicates that the line may contain the digits 4 or 5
S : indicates that the line may contain the digits 6 or 7
. : indicates that the line may contain the digits 8 or 9
A display may also allow 10 different digits (0 to 9) per line,
that is 1 line per stem, or just 1 digit per line, that is 10
lines per stem, as in the first of the three examples above.
Note that the median here is 4.5. This falls between two lines in
the first display but is highlighted on the second display since
it lies on a particular line.
Finally if there are positive and negative numbers on the display
these are highlighted by a + or - sign where the distinction is
required, that is near the zero point.
If there are too many leaves to fit in the plot width allowed,
G01ARF plots as many leaves as possible and places an asterisk to
the right to indicate that some leaves are not displayed. If this
occurs and the user wishes to be able to plot all the leaves then
the width of the plot may be adjusted.
Options also allow the leaf unit and the height of the display to
be specified by the user or calculated by G01ARF. These
parameters may be used to control the type of the display the
user wishes to obtain. Fixing the unit and changing the height of
the display may alter the number of lines used per stem, that is
the number of different digits per line. G01ARF will choose a
display for the fixed unit that attempts to make as much use of
the available height as possible, thus increasing the height may
allow for more lines per stem whereas decreasing the height may
force the display to use fewer lines per stem. Similarly the user
may wish to fix the height and vary the leaf digit unit used on
the display.
The display is returned in a character array with the option of
printing the display.
Parameters
g01arf
Required Input Arguments:
prt (1) string
y (:) real
Optional Input Arguments: <Default>
nstepx integer 35
nstepy integer 0
unit real 0
range (1) string 'e'
ldp integer 40
ifail integer -1
Output Arguments:
plot (1) (ldp,nstepx) string
lines integer
sorty (:) real
unit real
ifail integer