### 50.4 Functions and Variables for statistical graphs

Function: barsplot (data1, data2, …, option_1, option_2, …)

  Plots bars diagrams for discrete statistical variables, both for one or multiple samples.

  data can be a list of outcomes representing one sample, or a matrix of m rows and n columns, representing n samples of size m each.

  Available options are:

  - box_width (default, `3/4`): relative width of rectangles. This value must be in the range `[0,1]`.
  - grouping (default, `clustered`): indicates how multiple samples are shown. Valid values are: `clustered` and `stacked`.
  - groups_gap (default, `1`): a positive integer number representing the gap between two consecutive groups of bars.
  - bars_colors (default, `[]`): a list of colors for multiple samples. When there are more samples than specified colors, the extra necessary colors are chosen at random. See `color` to learn more about them.
  - frequency (default, `absolute`): indicates the scale of the ordinates. Possible values are: `absolute`, `relative`, and `percent`.
  - ordering (default, `orderlessp`): possible values are `orderlessp` or `ordergreatp`, indicating how statistical outcomes should be ordered on the x-axis.
  - sample_keys (default, `[]`): a list with the strings to be used in the legend. When the list length is other than 0 or the number of samples, an error message is returned.
  - start_at (default, `0`): indicates where the plot begins to be plotted on the x axis.
  - All global `draw` options, except `xtics`, which is internally assigned by `barsplot`. If you want to set your own values for this option or want to build complex scenes, make use of `barsplot_description`. See example below.
  - The following local draw-pkg options: `key`, `color_draw`, `fill_color`, `fill_density` and `line_width`. See also `barsplot`.

  There is also a function `wxbarsplot` for creating embedded histograms in interfaces wxMaxima and iMaxima. `barsplot` in a multiplot context.

  Examples:

  Univariate sample in matrix form. Absolute frequencies.

      (%i1) load ("descriptive")$
      (%i2) m : read_matrix (file_search ("biomed.data"))$

      (%i3) barsplot(
              col(m,2),
              title        = "Ages",
              xlabel       = "years",
              box_width    = 1/2,
              fill_density = 3/4)$

  Two samples of different sizes, with relative frequencies and user declared colors.

      (%i1) load ("descriptive")$
      (%i2) l1:makelist(random(10),k,1,50)$
      (%i3) l2:makelist(random(10),k,1,100)$

      (%i4) barsplot(
              l1,l2,
              box_width    = 1,
              fill_density = 1,
              bars_colors  = [black, grey],
              frequency = relative,
              sample_keys = ["A", "B"])$

  Four non numeric samples of equal size.

      (%i1) load ("descriptive")$

      (%i2) barsplot(
              makelist([Yes, No, Maybe][random(3)+1],k,1,50),
              makelist([Yes, No, Maybe][random(3)+1],k,1,50),
              makelist([Yes, No, Maybe][random(3)+1],k,1,50),
              makelist([Yes, No, Maybe][random(3)+1],k,1,50),
              title  = "Asking for something to four groups",
              ylabel = "# of individuals",
              groups_gap   = 3,
              fill_density = 0.5,
              ordering     = ordergreatp)$

  Stacked bars.

      (%i1) load ("descriptive")$

      (%i2) barsplot(
              makelist([Yes, No, Maybe][random(3)+1],k,1,50),
              makelist([Yes, No, Maybe][random(3)+1],k,1,50),
              makelist([Yes, No, Maybe][random(3)+1],k,1,50),
              makelist([Yes, No, Maybe][random(3)+1],k,1,50),
              title  = "Asking for something to four groups",
              ylabel = "# of individuals",
              grouping     = stacked,
              fill_density = 0.5,
              ordering     = ordergreatp)$

  For bars diagrams related options, see `barsplot` of package draw-pkg See also functions `histogram` and `piechart`.

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  Categories: Package descriptive ·Plotting

Function: barsplot_description (…)

  Function `barsplot_description` creates a graphic object suitable for creating complex scenes, together with other graphic objects.

  Example: `barsplot` in a multiplot context.

      (%i1) load ("descriptive")$
      (%i2) l1:makelist(random(10),k,1,50)$
      (%i3) l2:makelist(random(10),k,1,100)$
      (%i4) bp1 :
              barsplot_description(
               l1,
               box_width = 1,
               fill_density = 0.5,
               bars_colors = [blue],
               frequency = relative)$
      (%i5) bp2 :
              barsplot_description(
               l2,
               box_width = 1,
               fill_density = 0.5,
               bars_colors = [red],
               frequency = relative)$
      (%i6) draw(gr2d(bp1), gr2d(bp2))$

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  Categories: Package descriptive ·Plotting

Function: boxplot (data)
`boxplot` (data, option_1, option_2, …)

  This function plots box-and-whisker diagrams. Argument data can be a list, which is not of great interest, since these diagrams are mainly used for comparing different samples, or a matrix, so it is possible to compare two or more components of a multivariate statistical variable. But it is also allowed data to be a list of samples with possible different sample sizes, in fact this is the only function in package `descriptive` that admits this type of data structure.

  The box is plotted from the first quartile to the third, with an horizontal segment situated at the second quartile or median. By default, lower and upper whiskers are plotted at the minimum and maximum values, respectively. Option range can be used to indicate that values greater than `quantile(x,3/4)+range*(quantile(x,3/4)-quantile(x,1/4))` or less than `quantile(x,1/4)-range*(quantile(x,3/4)-quantile(x,1/4))` must be considered as outliers, in which case they are plotted as isolated points, and the whiskers are located at the extremes of the rest of the sample.

  Available options are:

  - box_width (default, `3/4`): relative width of boxes. This value must be in the range `[0,1]`.
  - box_orientation (default, `vertical`): possible values: `vertical` and `horizontal`.
  - range (default, `inf`): positive coefficient of the interquartilic range to set outliers boundaries.
  - outliers_size (default, `1`): circle size for isolated outliers.
  - All `draw` options, except `points_joined`, `point_size`, `point_type`, `xtics`, `ytics`, `xrange`, and `yrange`, which are internally assigned by `boxplot`. If you want to set your own values for this options or want to build complex scenes, make use of `boxplot_description`.
  - The following local `draw` options: `key`, `color`, and `line_width`.

  There is also a function `wxboxplot` for creating embedded histograms in interfaces wxMaxima and iMaxima.

  Examples:

  Box-and-whisker diagram from a multivariate sample.

      (%i1) load ("descriptive")$
      (%i2) s2 : read_matrix(file_search("wind.data"))$

      (%i3) boxplot(s2,
              box_width  = 0.2,
              title      = "Windspeed in knots",
              xlabel     = "Stations",
              color      = red,
              line_width = 2)$

  Box-and-whisker diagram from three samples of different sizes.

      (%i1) load ("descriptive")$

      (%i2) A :
             [[6, 4, 6, 2, 4, 8, 6, 4, 6, 4, 3, 2],
              [8, 10, 7, 9, 12, 8, 10],
              [16, 13, 17, 12, 11, 18, 13, 18, 14, 12]]$

      (%i3) boxplot (A, box_orientation = horizontal)$

  Option range can be used to handle outliers.

      (%i1) load ("descriptive")$
      (%i2) B: [[7, 15, 5, 8, 6, 5, 7, 3, 1],
                [10, 8, 12, 8, 11, 9, 20],
                [23, 17, 19, 7, 22, 19]] $

      (%i3) boxplot (B, range=1)$
      (%i4) boxplot (B, range=1.5, box_orientation = horizontal)$

      (%i5) draw2d(
              boxplot_description(
                B,
                range            = 1.5,
                line_width       = 3,
                outliers_size    = 2,
                color            = red,
                background_color = light_gray),
              xtics = {["Low",1],["Medium",2],["High",3]}) $

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  Categories: Package descriptive ·Plotting

Function: boxplot_description (…)

  Function `boxplot_description` creates a graphic object suitable for creating complex scenes, together with other graphic objects.

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  Categories: Package descriptive ·Plotting

Function: histogram
`histogram` (list)
`histogram` (list, option_1, option_2, …)
`histogram` (one_column_matrix)
`histogram` (one_column_matrix, option_1, option_2, …)
`histogram` (one_row_matrix)
`histogram` (one_row_matrix, option_1, option_2, …)

  This function plots an histogram from a continuous sample. Sample data must be stored in a list of numbers or an one dimensional matrix.

  Available options are:

  - nclasses (default, `10`): number of classes of the histogram, or a list indicating the limits of the classes and the number of them, or only the limits. This option also accepts bounds for varying bin widths, or a symbol with the name of one of the three optimal algorithms available for the number of classes: `'fd` (Freedman, D. and Diaconis, P. (1981) On the histogram as a density estimator: L_2 theory. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 57, 453-476.), `'scott` (Scott, D. W. (1979) On optimal and data-based histograms. Biometrika 66, 605-610.), and `'sturges` (Sturges, H. A. (1926) The choice of a class interval. Journal of the American Statistical Association 21, 65-66).
  - frequency (default, `absolute`): indicates the scale of the ordinates. Possible values are: `absolute`, `relative`, `percent`, and `density`. With `density`, the histogram area has a total area of one.
  - htics (default, `auto`): format of the histogram tics. Possible values are: `auto`, `endpoints`, `intervals`, or a list of labels.
  - All global `draw` options, except `xrange`, `yrange`, and `xtics`, which are internally assigned by `histogram`. If you want to set your own values for these options, make use of `histogram_description`. See examples bellow.
  - The following local draw-pkg options: `key`, `color`, `fill_color`, `fill_density` and `line_width`. See also `barsplot`.

  There is also a function `wxhistogram` for creating embedded histograms in interfaces wxMaxima and iMaxima.

  Examples:

  A simple with eight classes:

      (%i1) load ("descriptive")$
      (%i2) s1 : read_list (file_search ("pidigits.data"))$
      (%i3) histogram (
                 s1,
                 nclasses     = 8,
                 title        = "pi digits",
                 xlabel       = "digits",
                 ylabel       = "Absolute frequency",
                 fill_color   = grey,
                 fill_density = 0.6)$

  Setting the limits of the histogram to -2 and 12, with 3 classes. Also, we introduce predefined tics:

      (%i1) load ("descriptive")$
      (%i2) s1 : read_list (file_search ("pidigits.data"))$
      (%i3) histogram (
                 s1,
                 nclasses     = [-2,12,3],
                 htics        = ["A", "B", "C"],
                 terminal     = png,
                 fill_color   = "#23afa0",
                 fill_density = 0.6)$

  Bounds for varying bin widths.

      (%i1) load ("descriptive")$
      (%i2) s1 : read_list (file_search ("pidigits.data"))$
      (%i3) histogram (s1, nclasses = {0,3,6,7,11})$

  Freedmann - Diakonis robust method for optimal search of the number of classes.

      (%i1) load ("descriptive")$
      (%i2) s1 : read_list (file_search ("pidigits.data"))$
      (%i3) histogram(s1, nclasses=fd) $

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  Categories: Package descriptive ·Plotting

Function: histogram_description (…)

  Function `histogram_description` creates a graphic object suitable for creating complex scenes, together with other graphic objects. We make use of `histogram_description` for setting the `xrange` and adding an explicit curve into the scene:

      (%i1) load ("descriptive")$
      (%i2) ( load("distrib"),
              m: 14, s: 2,
              s2: random_normal(m, s, 1000) ) $
      (%i3) draw2d(
              grid   = true,
              xrange = [5, 25],
              histogram_description(
                s2,
                nclasses     = 9,
                frequency    = density,
                fill_density = 0.5),
              explicit(pdf_normal(x,m,s), x, m - 3*s, m + 3* s))$

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  Categories: Package descriptive ·Plotting

Function: piechart
`piechart` (list)
`piechart` (list, option_1, option_2, …)
`piechart` (one_column_matrix)
`piechart` (one_column_matrix, option_1, option_2, …)
`piechart` (one_row_matrix)
`piechart` (one_row_matrix, option_1, option_2, …)

  Similar to `barsplot`, but plots sectors instead of rectangles.

  Available options are:

  - sector_colors (default, `[]`): a list of colors for sectors. When there are more sectors than specified colors, the extra necessary colors are chosen at random. See `color` to learn more about them.
  - pie_center (default, `[0,0]`): diagram’s center.
  - pie_radius (default, `1`): diagram’s radius.
  - All global `draw` options, except `key`, which is internally assigned by `piechart`. If you want to set your own values for this option or want to build complex scenes, make use of `piechart_description`.
  - The following local `draw` options: `key`, `color`, `fill_density` and `line_width`. See also `ellipse`

  There is also a function `wxpiechart` for creating embedded histograms in interfaces wxMaxima and iMaxima.

  Example:

      (%i1) load ("descriptive")$
      (%i2) s1 : read_list (file_search ("pidigits.data"))$
      (%i3) piechart(
              s1,
              xrange  = [-1.1, 1.3],
              yrange  = [-1.1, 1.1],
              title   = "Digit frequencies in pi")$

  See also function `barsplot`.

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  Categories: Package descriptive ·Plotting

Function: piechart_description (…)

  Function `piechart_description` creates a graphic object suitable for creating complex scenes, together with other graphic objects.

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  Categories: Package descriptive ·Plotting

Function: scatterplot
`scatterplot` (list)
`scatterplot` (list, option_1, option_2, …)
`scatterplot` (matrix)
`scatterplot` (matrix, option_1, option_2, …)

  Plots scatter diagrams both for univariate (list) and multivariate (matrix) samples.

  Available options are the same admitted by `histogram`.

  There is also a function `wxscatterplot` for creating embedded histograms in interfaces wxMaxima and iMaxima.

  Examples:

  Univariate scatter diagram from a simulated Gaussian sample.

      (%i1) load ("descriptive")$
      (%i2) load ("distrib")$

      (%i3) scatterplot(
              random_normal(0,1,200),
              xaxis      = true,
              point_size = 2,
              dimensions = [600,150])$

  Two dimensional scatter plot.

      (%i1) load ("descriptive")$
      (%i2) s2 : read_matrix (file_search ("wind.data"))$

      (%i3) scatterplot(
             submatrix(s2, 1,2,3),
             title      = "Data from stations #4 and #5",
             point_type = diamant,
             point_size = 2,
             color      = blue)$

  Three dimensional scatter plot.

      (%i1) load ("descriptive")$
      (%i2) s2 : read_matrix (file_search ("wind.data"))$
      (%i3) scatterplot(submatrix (s2, 1,2), nclasses=4)$

  Five dimensional scatter plot, with five classes histograms.

      (%i1) load ("descriptive")$
      (%i2) s2 : read_matrix (file_search ("wind.data"))$

      (%i3) scatterplot(
              s2,
              nclasses     = 5,
              frequency    = relative,
              fill_color   = blue,
              fill_density = 0.3,
              xtics        = 5)$

  For plotting isolated or line-joined points in two and three dimensions, see `points`. See also `histogram`.

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  Categories: Package descriptive ·Plotting

Function: scatterplot_description (…)

  Function `scatterplot_description` creates a graphic object suitable for creating complex scenes, together with other graphic objects.

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  Categories: Package descriptive ·Plotting

Function: starplot (data1, data2, …, option_1, option_2, …)

  Plots star diagrams for discrete statistical variables, both for one or multiple samples.

  data can be a list of outcomes representing one sample, or a matrix of m rows and n columns, representing n samples of size m each.

  Available options are:

  - stars_colors (default, `[]`): a list of colors for multiple samples. When there are more samples than specified colors, the extra necessary colors are chosen at random. See `color` to learn more about them.
  - frequency (default, `absolute`): indicates the scale of the radii. Possible values are: `absolute` and `relative`.
  - ordering (default, `orderlessp`): possible values are `orderlessp` or `ordergreatp`, indicating how statistical outcomes should be ordered.
  - sample_keys (default, `[]`): a list with the strings to be used in the legend. When the list length is other than 0 or the number of samples, an error message is returned.
  - star_center (default, `[0,0]`): diagram’s center.
  - star_radius (default, `1`): diagram’s radius.
  - All global `draw` options, except `points_joined`, `point_type`, and `key`, which are internally assigned by `starplot`. If you want to set your own values for this options or want to build complex scenes, make use of `starplot_description`.
  - The following local `draw` option: `line_width`.

  There is also a function `wxstarplot` for creating embedded histograms in interfaces wxMaxima and iMaxima.

  Example:

  Plot based on absolute frequencies. Location and radius defined by the user.

      (%i1) load ("descriptive")$
      (%i2) l1: makelist(random(10),k,1,50)$
      (%i3) l2: makelist(random(10),k,1,200)$

      (%i4) starplot(
              l1, l2,
              stars_colors = [blue,red],
              sample_keys = ["1st sample", "2nd sample"],
              star_center = [1,2],
              star_radius = 4,
              proportional_axes = xy,
              line_width = 2 ) $

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  Categories: Package descriptive ·Plotting

Function: starplot_description (…)

  Function `starplot_description` creates a graphic object suitable for creating complex scenes, together with other graphic objects.

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  Categories: Package descriptive ·Plotting

Function: stemplot
`stemplot` (data)
`stemplot` (data, option)

  Plots stem and leaf diagrams.

  Unique available option is:

  - leaf_unit (default, `1`): indicates the unit of the leaves; must be a power of 10.

  Example:

      (%i1) load ("descriptive")$
      (%i2) load(distrib)$

      (%i3) stemplot(
              random_normal(15, 6, 100),
              leaf_unit = 0.1);
      -5|4
       0|37
       1|7
       3|6
       4|4
       5|4
       6|57
       7|0149
       8|3
       9|1334588
      10|07888
      11|01144467789
      12|12566889
      13|24778
      14|047
      15|223458
      16|4
      17|11557
      18|000247
      19|4467799
      20|00
      21|1
      22|2335
      23|01457
      24|12356
      25|455
      27|79
      key: 6|3 =  6.3
      (%o3)                  done

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  Categories: Package descriptive ·Plotting