GUImad

GUImad shows the necessary calculations to obtain MAD, S_M or S_Me in a GUI.

Syntax

Description

This routine shows all the intermediate necessary steps to compute the three following variability indexes:

\[ MAD =Me(|x_{i} - Me|n_i). \] \[ S_{M} = \frac{\sum_{i=1}^{r}|x_{i}-M| n_i}{n} \] \[ S_{Me} = \frac{\sum_{i=1}^r |x_i-Me|n_i}{n}. \]

example

out =GUImad(x) Example of calculation of MAD.

example

out =GUImad(x, flag) Example of calculation of SMe.

example

out =GUImad(x, flag, w) Example of calculation of SM.

Examples

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  • Example of calculation of MAD.
  • MAD = median absolute deviation from median.

    x=[98 105 85 110 102];
    y=GUImad(x);

  • Example of calculation of SMe.
  • SMe= mean absolute deviation from the median.

    x=[98 105 85 110 102];
    y=GUImad(x,2);

  • Example of calculation of SM.
  • SM= mean absolute deviation from mean.

    x=[98 105 85 110 102];
    y=GUImad(x,0);

    Related Examples

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  • MAD in a frequency distribution.
  • MAD = median absolute deviation from median.

    % Frequency distribution of the number of children in a sample of 400
    % families. (See page 29 of [CMR]).
    X=[0	112
    1	156
    2	111
    3	16
    4	4
    7	1];
    x=X(:,1);
    freq=X(:,2);
    flag=1;
    GUImad(x,flag,freq);
    Click here for the graphical output of this example (link to Ro.S.A. website)

  • SM in a frequency distribution.
  • SM= mean absolute deviation from mean.

    % Frequency distribution of the number of children in a sample of 400
    % families. (See page 29 of [CMR]).
    X=[0	112
    1	156
    2	111
    3	16
    4	4
    7	1];
    x=X(:,1);
    freq=X(:,2);
    flag=0;
    GUImad(x,flag,freq);
    Click here for the graphical output of this example (link to Ro.S.A. website)

  • SMe in a frequency distribution.
  • SMe= median absolute deviation from mean.

    % Frequency distribution of the number of children in a sample of 400 families. (See page 29 of [CMR]).
    X=[0	112
    1	156
    2	111
    3	16
    4	4
    7	1];
    x=X(:,1);
    freq=X(:,2);
    flag=2;
    GUImad(x,flag,freq);
    Click here for the graphical output of this example (link to Ro.S.A. website)

    Input Arguments

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    x — vector of numeric data. Vector.

    Vector containing strictly numerical data.

    Data Types: double

    Optional Arguments

    flag — median or mean absolute deviation from median or mean absolute deviation from mean. Scalar.

    If flag=1 (default), MAD is based on medians, i.e. median(abs(x-median(x)).

    elseif flag=0, $S_M$ is computed (mean absolute deviation) i.e. mean(abs(x-mean(x)).

    elseif flag=2, $S_{Me}$ is computed (mean absolute deviation from median) i.e. mean(abs(x-median(x)).

    Example: 1

    Data Types: double

    w — weights. Vector.

    Vector of the same length of x containing the weights assigned to each observation.

    Example: 1:10

    Data Types: double

    Output Arguments

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    out —detailed output to compute the index. Table

    Table with n+1 rows (where n is the length of x) containing what is shown in the GUI. Last row contains the totals.

    References

    Cerioli, A., Milioli, M.A., Riani, M. (2016), "Esercizi di statistica (Quinta edizione)". [CMR]

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