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Chapter Contents
Chapter Introduction
NAG Toolbox

NAG Toolbox: nag_stat_5pt_summary (g01al)


    1  Purpose
    2  Syntax
    7  Accuracy
    9  Example


nag_stat_5pt_summary (g01al) calculates a five-point summary for a single sample.


[res, ifail] = g01al(x, 'n', n)
[res, ifail] = nag_stat_5pt_summary(x, 'n', n)


nag_stat_5pt_summary (g01al) calculates the minimum, lower hinge, median, upper hinge and the maximum of a sample of n observations.
The data consist of a single sample of n observations denoted by xi and let zi, for i=1,2,,n, represent the sample observations sorted into ascending order.
Let m= n2  if n is even and n+1 2  if n is odd,
and k= m2  if m is even and m+1 2  if m is odd.
Then we have
Minimum =z1,  
Maximum =zn,  
Median =zm if n is odd,
  = zm+zm+12 if n is even, 12
Lower hinge =zk if m is odd,
  = zk+zk+12 if m is even, 12
Upper hinge =zn-k+1 if m is odd,
  = zn-k+zn-k+12 if m is even. 12


Erickson B H and Nosanchuk T A (1985) Understanding Data Open University Press, Milton Keynes
Tukey J W (1977) Exploratory Data Analysis Addison–Wesley


Compulsory Input Parameters

1:     xn – double array
The sample observations, x1,x2,,xn.

Optional Input Parameters

1:     n int64int32nag_int scalar
Default: the dimension of the array x.
n, number of observations in the sample.
Constraint: n5.

Output Parameters

1:     res5 – double array
res contains the five-point summary.
The minimum.
The lower hinge.
The median.
The upper hinge.
The maximum.
2:     ifail int64int32nag_int scalar
ifail=0 unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:
On entry,n<5.
An unexpected error has been triggered by this routine. Please contact NAG.
Your licence key may have expired or may not have been installed correctly.
Dynamic memory allocation failed.


The computations are stable.

Further Comments

The time taken by nag_stat_5pt_summary (g01al) is proportional to n.


This example calculates a five-point summary for a sample of 12 observations.
function g01al_example

fprintf('g01al example results\n\n');

x = [12     9     2     5     6     8 ...
      2     7     3     1    11    10];

[res, ifail] = g01al(x);

fprintf('Maximum                    %14.4f\n', res(5));
fprintf('Upper Hinge (75%% quantile) %14.4f\n', res(4));
fprintf('Median      (50%% quantile) %14.4f\n', res(3));
fprintf('Lower Hinge (25%% quantile) %14.4f\n', res(2));
fprintf('Minimum                    %14.4f\n', res(1));

g01al example results

Maximum                           12.0000
Upper Hinge (75% quantile)         9.5000
Median      (50% quantile)         6.5000
Lower Hinge (25% quantile)         2.5000
Minimum                            1.0000

PDF version (NAG web site, 64-bit version, 64-bit version)
Chapter Contents
Chapter Introduction
NAG Toolbox

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